#1**+1 **

Alright, first let's note that we can caluclate the number of distinct arrangements through the equation

\(\text{Number of Distinct Arrangements} = \frac{n!}{n_1! \cdot n_2! \cdot n_3! ... \cdot n_k!}\)

where n is the total number of items to arrange, and n1,n2,…,nk are the frequencies of the distinct items (for example, i in mississippi appears 4 times).

Thus, let's list our the letters we have in the word.

Mississippi has 11 letters, so n is 11.

In the word, i appears 4 times, m appears once, s appears twice, and p appears twice.

Thus, plugging in all these numbers, we have

\(\frac{11!}{1! \cdot 4! \cdot 2! \cdot 21} = 34650\)

So 34650 is our answer.

Thanks! :)

NotThatSmart Aug 13, 2024