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Chapter 4: Q22 (page 175)

In Exercises 5鈥�36, express all probabilities as fractions.

Classic Counting Problem A classic counting problem is to determine the number of different ways that the letters of 鈥淢ississippi鈥� can be arranged. Find that number.

Short Answer

Expert verified

The number of different (unique) ways in which the letters of the word 鈥淢ississippi鈥� can be arranged is 34650.

Step by step solution

01

Given information

The letters of the word 鈥淢ississippi鈥� have to be arranged.

02

Permutation in the case of repetition of letters

Several different permutations/arrangements can be made for n units if n1 are of one type, n2 are of another type, and so on.

n!n1!脳n2!脳...

03

Compute the number of ways different arrangements for the letters

The total number of letters (n) is 11.

The number of times the letter 鈥渋鈥� is repeated is 4.

The number of times the letter 鈥渟鈥� is repeated is 4.

The number of times the letter 鈥減鈥� is repeated is 2.

The total number of permutations possible to arrange the letters of the word 鈥淢ississippi鈥� is given as follows:

11!4!脳4!脳2!=11脳10脳9脳8脳7脳6脳5脳4!4!脳4脳3脳2脳1脳2脳1=34650

Therefore, the number of different ways in which the letters of the word 鈥淢ississippi鈥� can be arranged is 34650.

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