Question

How many different "words" can you make using all the letters of the word MISSISSIPPI if
a) there are no restrictions?
b) the word must end with an I?
c) the word cannot end in an I?

Answer 1

a) The word “MISSISSIPPI” consists of 11 letters: “M”= 1 letter, “I”= 4 letters, “S”= 4 letters, “P”= 2 letters.

“Word” is permutation of letters. We will use formula for permutations with identical elements to find number of different permutations.

The number of permutations of $n$ elements with $n_1$ identical elements of type 1, n_2 \ identical elements of type 2, …, and $n_k$ identical elements of type k is

$\frac{n!}{n_1!n_2!…n_k!}$

So, the number of different words is $\frac{11!}{1!\cdot4!\cdot4!\cdot 2!}=34\ 650$

Answer: 34 650 words.

b) The 11th letter is known, it must be “I”. Therefore, we need to find number of different words that consist of 10 letters: “M”= 1 letter, “I”= 3 letters, “S”= 4 letters, “P”= 2 letters.

Using the formula from part (a), we have:

The number of words is $\frac{10!}{1!\cdot3!\cdot4!\cdot 2!}=12\ 600$

Answer: 12600 words.

c) We’ve calculated number of words that end with “I”. So, other words cannot end with “I”.

The number of such words is $34\ 650-12\ 600= 22\ 050$

Answer: 22 050 words.