The formula for multinomial expansion is (a + b + c + ...)^n = ∑ n!/(p!q!r!...) * ap * bq * cr * ..., where a, b, c, etc. represent the terms and p, q, r, etc. represent the number of times each term is repeated.
There are 1,386 combinations of letters that can be formed from the word MISSISSIPPI taken 5 at a time.
The word “multinomial” refers to an algebraic expression with more than two terms. In multinomial expansion, we are expanding an expression with multiple terms raised to a power.
One example of multinomial expansion using the word MISSISSIPPI taken 5 at a time is (M + I + S + S + I + S + S + I + P + P + I)^5 = 201,553,707,440,000.
Multinomial expansion is an extension of the binomial theorem, which is used to expand expressions with two terms raised to a power. The binomial theorem can be seen as a special case of multinomial expansion, where there are only two terms (a and b) being raised to a power.