{"id":1021,"date":"2023-07-27T23:10:51","date_gmt":"2023-07-27T23:10:51","guid":{"rendered":"https:\/\/statorials.org\/my\/multinomial-coefficient\/"},"modified":"2023-07-27T23:10:51","modified_gmt":"2023-07-27T23:10:51","slug":"multinomial-coefficient","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/multinomial-coefficient\/","title":{"rendered":"Multinomial coefficient- \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1014\u103e\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038"},"content":{"rendered":"

<\/p>\n

\n

Multinomial coefficient<\/strong> \u101e\u100a\u103a n<\/em> objects \u1019\u103b\u102c\u1038\u104f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031\u101b\u103e\u102d\u101e\u1031\u102c partition \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a n 1<\/sub><\/em> , n 2<\/sub><\/em> , \u2026, n k<\/sub><\/em> \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038<\/em> \u101e\u102d\u102f\u1037 \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n

Multinomial coefficient \u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1019\u103e\u102c-<\/span><\/p>\n

Multinomial coefficient = n \u104b \/ (n 1<\/sub> ! * n 2<\/sub> ! * \u2026 * n k<\/sub> !)<\/span><\/p>\n

\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a \u1018\u1000\u103a\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1025\u1015\u1019\u102c 1- \u1005\u1000\u102c\u1038\u101c\u102f\u1036\u1038\u1010\u1005\u103a\u101c\u102f\u1036\u1038\u1010\u103d\u1004\u103a \u1005\u102c\u101c\u102f\u1036\u1038\u1019\u103b\u102c\u1038<\/strong><\/span><\/h3>\n

ARKANSAS \u101f\u1030\u101e\u1031\u102c \u1005\u1000\u102c\u1038\u101c\u102f\u1036\u1038\u104f \u1011\u1030\u1038\u1001\u103c\u102c\u1038\u101e\u1031\u102c\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1019\u100a\u103a\u1019\u103b\u103e\u101b\u103e\u102d\u101e\u1014\u100a\u103a\u1038\u104b<\/span><\/p>\n

\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u1001\u103b\u1000\u103a-<\/strong> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u1000\u103a\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1010\u103d\u1004\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u1005\u103d\u102c\u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n

n<\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u102c\u101c\u102f\u1036\u1038\u1019\u103b\u102c\u1038) : \u1048<\/span><\/p>\n

n 1<\/sub><\/strong> (\u1021\u1000\u1039\u1001\u101b\u102c \u201cA\u201d): \u1043<\/span><\/p>\n

n 2<\/sub><\/strong> (\u1021\u1000\u1039\u1001\u101b\u102c \u201cR\u201d): \u1041<\/span><\/p>\n

n 3<\/sub><\/strong> (\u1021\u1000\u1039\u1001\u101b\u102c \u201cK\u201d): \u1041<\/span><\/p>\n

n 4<\/sub><\/strong> (\u1021\u1000\u1039\u1001\u101b\u102c \u201cN\u201d): \u1041<\/span><\/p>\n

n 5<\/sub><\/strong> (\u1021\u1000\u1039\u1001\u101b\u102c \u201cS\u201d): \u1042<\/span><\/p>\n

Multinomial coefficient = 8\u104b \/ (3!*1!*1!*1!*2!) = 3.360\u104a<\/strong><\/span><\/p>\n

ARKANSAS \u101f\u1030\u101e\u1031\u102c\u1005\u1000\u102c\u1038\u101c\u102f\u1036\u1038\u104f\u1011\u1030\u1038\u1001\u103c\u102c\u1038\u101e\u1031\u102c\u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103d\u1032\u1015\u1031\u102b\u1004\u103a\u1038 3,360<\/strong> \u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1025\u1015\u1019\u102c 2- \u1005\u102c\u101e\u1004\u103a\u1014\u103e\u1005\u103a\u1021\u101c\u102d\u102f\u1000\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038<\/strong><\/span><\/h3>\n

\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 \u1001\u103c\u1031\u102c\u1000\u103a\u101a\u1031\u102c\u1000\u103a\u1015\u102b\u1010\u1032\u1037 \u1021\u1016\u103d\u1032\u1037\u1000\u102d\u102f \u1021\u1000\u103c\u102e\u1038\u1010\u1014\u103a\u1038 \u1043 \u101a\u1031\u102c\u1000\u103a\u104a \u1021\u1004\u101a\u103a\u1010\u1014\u103a\u1038 \u1042 \u101a\u1031\u102c\u1000\u103a\u1014\u1032\u1037 \u1012\u102f\u1010\u102d\u101a\u1010\u1014\u103a\u1038 \u1041 \u101a\u1031\u102c\u1000\u103a\u1014\u1032\u1037 \u1016\u103d\u1032\u1037\u1005\u100a\u103a\u1038\u1011\u102c\u1038\u1015\u102b\u1010\u101a\u103a\u104b \u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u101c\u103b\u103e\u1004\u103a \u1024\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103e \u1011\u1030\u1038\u1001\u103c\u102c\u1038\u101e\u1031\u102c\u101b\u1019\u103e\u1010\u103a\u1019\u100a\u103a\u1019\u103b\u103e\u101b\u103e\u102d\u101e\u1014\u100a\u103a\u1038\u104b<\/span><\/p>\n

\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u1001\u103b\u1000\u103a-<\/strong> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u1000\u103a\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1010\u103d\u1004\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u1005\u103d\u102c\u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n

n<\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038 \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038) \u1046<\/span><\/p>\n

n 1<\/sub><\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038 \u101e\u1000\u103a\u1000\u103c\u102e\u1038\u101b\u103d\u101a\u103a\u1021\u102d\u102f\u1019\u103b\u102c\u1038): 3<\/span><\/p>\n

n 2<\/sub><\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1021\u1004\u101a\u103a\u1010\u1014\u103a\u1038): 2<\/span><\/p>\n

n 3<\/sub><\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038 \u1012\u102f\u1010\u102d\u101a\u1014\u103e\u1005\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038) \u1041<\/span><\/p>\n

Multinomial coefficient = 6\u104b \/ (3!*2!*1!) = 60<\/strong><\/span><\/p>\n

\u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1024\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1011\u1036\u1019\u103e \u1011\u1030\u1038\u1001\u103c\u102c\u1038\u101e\u1031\u102c\u101b\u1019\u103e\u1010\u103a 60<\/strong> \u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1025\u1015\u1019\u102c \u1043- \u1014\u102d\u102f\u1004\u103a\u1004\u1036\u101b\u1031\u1038\u1015\u102b\u1010\u102e \u1026\u1038\u1005\u102c\u1038\u1015\u1031\u1038<\/strong><\/span><\/h3>\n

\u1001\u101b\u102d\u102f\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1014\u1031\u1011\u102d\u102f\u1004\u103a\u101e\u1030\u1006\u101a\u103a\u1026\u1038\u1021\u1014\u1000\u103a \u1043 \u1026\u1038\u1019\u103e\u102c \u101b\u102e\u1015\u1010\u103a\u1018\u101c\u1005\u103a\u1000\u1014\u103a\u1019\u103b\u102c\u1038\u104a \u1012\u102e\u1019\u102d\u102f\u1000\u101b\u1000\u103a\u1010\u1005\u103a\u1015\u102b\u1010\u102e\u1019\u103e \u1045 \u1026\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u1005\u103a\u101e\u102e\u1038\u1015\u102f\u1002\u1039\u1002\u101c \u1042 \u1026\u1038\u1010\u102d\u102f\u1037\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u100c\u102c\u1014\u1031\u1021\u1016\u103d\u1032\u1037\u1010\u103d\u1004\u103a \u1014\u102d\u102f\u1004\u103a\u1004\u1036\u101b\u1031\u1038\u1015\u102b\u1010\u102e\u1019\u103e \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1019\u100a\u103a\u1019\u103b\u103e\u101b\u103e\u102d\u101e\u1014\u100a\u103a\u1038\u104b<\/span><\/p>\n

\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u1001\u103b\u1000\u103a-<\/strong> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u1000\u103a\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1010\u103d\u1004\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u1005\u103d\u102c\u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n

n<\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1014\u1031\u1011\u102d\u102f\u1004\u103a\u101e\u1030) \u1041\u1040<\/span><\/p>\n

n 1<\/sub><\/strong> (\u101b\u102e\u1015\u1010\u103a\u1018\u101c\u1005\u103a\u1000\u1014\u103a\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038) 3<\/span><\/p>\n

\u1014\u1036\u1015\u102b\u1010\u103a \u1042<\/sub><\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038 \u1012\u102e\u1019\u102d\u102f\u1000\u101b\u1000\u103a\u1019\u103b\u102c\u1038) \u1045<\/span><\/p>\n

n 3<\/sub><\/strong> (\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038 \u1010\u1005\u103a\u101e\u102e\u1038\u1015\u102f\u1002\u1039\u1002\u101c): \u1042<\/span><\/p>\n

Multinomial coefficient = 10\u104b \/ (3!*5!*2!) = 2.520<\/strong><\/span><\/p>\n

\u1014\u102d\u102f\u1004\u103a\u1004\u1036\u101b\u1031\u1038 \u1015\u102b\u1010\u102e \u1021\u101c\u102d\u102f\u1000\u103a \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038 \u1005\u102d\u1010\u103a\u1016\u103c\u102c \u1019\u103e\u102f \u1042,\u1045\u1042\u1040<\/strong> \u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h3>\n

\u101b\u101c\u1012\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1015\u102f\u1036\u101e\u1031\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101b\u103e\u102d\u101e\u100a\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f k<\/em> \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u1031\u102c\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1010\u102d\u1000\u103b\u101e\u1031\u102c\u101b\u1031\u1010\u103d\u1000\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u101b\u101b\u103e\u102d\u1001\u103c\u1004\u103a\u1038\u104f\u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1000\u102d\u102f\u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a multinomial \u1016\u103c \u1014\u1037\u103a\u1016\u103c\u1030\u1038<\/a> \u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a\u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u104f\u1010\u1005\u103a\u1005\u102d\u1010\u103a\u1010\u1005\u103a\u1015\u102d\u102f\u1004\u103a\u1038\u104c \u1018\u1000\u103a\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1021\u1015\u102d\u102f\u1006\u102f-<\/strong> Multinomial Coefficients Calculator \u1000\u102d\u102f \u101e\u1004\u103a \u1021\u101c\u103d\u101a\u103a\u1010\u1000\u1030 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a Multinomial Coefficients \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Multinomial coefficient \u101e\u100a\u103a n objects \u1019\u103b\u102c\u1038\u104f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103b\u1031\u101b\u103e\u102d\u101e\u1031\u102c partition \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a n 1 , n 2 , \u2026, n k \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038 \u101e\u102d\u102f\u1037 \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b Multinomial coefficient \u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u1019\u103e\u102c- Multinomial coefficient = n \u104b \/ (n 1 ! * n 2 ! * \u2026 * n k !) \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a \u1018\u1000\u103a\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c 1- \u1005\u1000\u102c\u1038\u101c\u102f\u1036\u1038\u1010\u1005\u103a\u101c\u102f\u1036\u1038\u1010\u103d\u1004\u103a \u1005\u102c\u101c\u102f\u1036\u1038\u1019\u103b\u102c\u1038 ARKANSAS […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"\nMultinomial coefficient- \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1014\u103e\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038 - Statology<\/title>\n<meta name=\"description\" content=\"\u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1005\u103d\u102c \u1021\u1015\u102b\u1021\u101d\u1004\u103a \u1021\u1019\u100a\u103a\u1019\u103b\u102d\u102f\u1038\u1005\u102f\u1036\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u104f \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/my\/multinomial-coefficient\/\" \/>\n<meta property=\"og:locale\" content=\"my_MM\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Multinomial coefficient- 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