You can paste numbers separated by commas, spaces, or newlines. The sum of all numbers will be the total (n).
Result
M(n; k₁,k₂,...)
=
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About Multinomial Coefficients
The multinomial coefficient calculates the number of ways to divide n distinct objects into k groups, where each group i contains kᵢ objects.
Formula:
\[\binom{n}{k_1,k_2,\ldots,k_m} = \frac{n!}{k_1!k_2!\cdots k_m!}\]
For example:
- For n=6 divided into groups of (2,2,2): \(\binom{6}{2,2,2} = \frac{6!}{2!2!2!} = 90\)
- For n=5 divided into groups of (3,2): \(\binom{5}{3,2} = \frac{5!}{3!2!} = 10\)
Applications include:
- Probability theory and statistics
- Permutations with repeated elements
- Polynomial expansions
- Combinatorial problems in computer science
Note: The sum of all group sizes must equal the total number of objects (n).