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Chapter 11: Problem 52

How many distinct permutations can be formed using the letters of the word TENNESSEE?

Short Answer

Expert verified
The number of distinct permutations of the word TENNESSEE is 15,120.

Step by step solution

01

Identify Repeated Letters and Total Letters

Firstly, count the number of each letter in the word: 1 T, 4 E, 2 N and 2 S. This sums up to a total of 9 letters.
02

Determine Total Distinct Permutations

The total distinct permutations of a word is given by the factorial of the total letters in the word divided by the product of the factorials of the frequency of each letter. Hence, the formula to be used is: \( \frac{9!}{1! 4! 2! 2!} \). Calculate this value to determine the number of distinct permutations.
03

Calculate Factorials

Calculate the factorials for 9, 4, 2 and 1. Factorial of a number \( n \), denoted by \( n! \), is the product of all positive integers less than or equal to \( n \). For example, 3! = 3*2*1 = 6.
04

Substitute calculated values into formula

Substitute the calculated factorials into the formula: \( \frac{9!}{1! 4! 2! 2!} = \frac{362880}{(1*24*2*2)} \). Execute this calculation to find the final answer.

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