Question

from the letters of each of the following words, how many different permutations can be formed if the letters are taken all at a time

Answer 1

And, the word is ?

Answer 2

What is the word?

Answer 3

Mississippi. Im so sorry.

Answer 4

First, a smaller example.
Question: What is the number of different 4-letter "words" that can be made from the word NOON?

There are 4 choices for the first letter, 3 for the second, 2 for the third, and 1 for the fourth letter. That would give 4*3*2*1 or 24 possible "words." But, some of those 24 words are duplicates because the word NOON contains two Ns and two Os and they are indistinguishable.

We would have to divide out the repetitions. This action would give a final answer of 4!/(2!*2!) = 6 different words. You can write these out to convince yourself.

Answer 5

In Mississippi, there are 11 letters. That gives 11! permutations of the 11 letters. But, because there are 4 s, 4 i, and 2 p letters, some of the 11! permutations will be duplicates. Those must be divided out.

The number of 11 letter permuation of the letters of the word Mississippi is the following: 11! / (4!*4!*2!).
@senga