Question

How many distinct ways can we rearrange the letters in the word mississippi?

Answer 1

There are 34,650 distinct ways to rearrange the letters in the word mississippi, calculated by the formula for permutations of a multiset.

Step-by-step explanation:

To determine the number of distinct ways to rearrange the letters in the word mississippi, we need to use the formula for permutations of multiset. The word mississippi contains 11 letters with 1 'm', 4 'i's, 4 's's, and 2 'p's. Using the formula, which is the factorial of the total number of letters divided by the factorial of the number of each repeated letter, we get:

Permutations = ℑ! / (m!i!s!p!)

Where ℑ is the total number of letters, m is the number of 'm's, i is the number of 'i's, s is the number of 's's, and p is the number of 'p's. Plugging in the values we get:

Permutations = 11! / (1!4!4!2!) = 34,650.

Therefore, there are 34,650 distinct ways to rearrange the letters in the word mississippi.