What is the total number of different combinations of names that can be made from the letters of the word "MISSISSIPPI," using all the letters at a time?

The word MISSISSIPPI contains 11 letters in total, consisting of 4 instances of S, 4 instances of I, 2 instances of P, and 1 instance of M. To find the distinct combinations using all the letters, we use the permutation formula for a multiset, dividing the total number of letters factorial by the factorial of each repeating letter's frequency. The calculation is 11 factorial divided by the product of 4 factorial, 4 factorial, and 2 factorial, resulting in 11! / (4! × 4! × 2!).

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