Question

A classic counting problem is to determine the number of different ways that the letters of "Mississippi"can be arranged. Find that number.

Answer 1

34, 650

Explanation:

Given that,

The word = Mississippi

To find,

No. of different ways in which the letters of this word can be arranged = ?

Procedure:

Using the permutation rule as it is the case of repetition of identical items for finding the possibilities.

No. of letters in 'Mississippi' = 11

Letter 'i' appears = 4 times

Letter 's' appears = 4 times

Letter 'm' appears = 1 time

Letter 'p' appears = 2 times

So,

No. of possibilities = 11 ! ÷ (4 ! 4 ! 1 ! 2 !)

= (11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 *1)/(4 * 3 *2 * 1)(4 * 3 *2 * 1)(1)(2 * 1)

= 11 * 10 * 9 * 7 * 5

= 34,650