How many distinct ways can all the letters in MISSISSIPPI be arranged to form a new word?
Before we answer this, let’s do something simpler; the number of ways of arranging the word CAT. It can form CAT, CTA, TCA, TAC, ACT, and ATC; in six ways.
We can also use the permutation formula to arrive at the same. Why permutation? Well, the order matters here, or else it would have been only one combination possible. So, 3P3 = 3!/0! = 3! = 3 x 2 x 1 = 6.
MISSISSIPPI
There are 11 letters in the word MISSISSIPPI. So it is 11!. But some of the letters are the same. There are four Is, four Ss and two Ps in it. You don’t want multiple-count the repeated ones. The way to avoid it is to divide the original permutations (11!) with the respective repeated permutations. So the required value is
11!/(4!4!2!) = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4! /(4! x 4 x 3 x 2 x 1 x 2 x 1)
= 11 x 10 x 9 x 7 x 5 = 34650.
