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Chapter 33: Problem 1071

In how many ways can letters of the word "tennessee" be arrenged?

Short Answer

Expert verified
There are 15,120 ways to arrange the letters of the word "tennessee", taking into account the repetitions of letters.

Step by step solution

01

Identify the number of repetitions of each letter

In the word "tennessee", there are - 4 times the letter 'e' - 3 times the letter 'n' - 2 times the letter 's' - 1 time the letter 't'
02

Calculate the total number of permutations without taking repetitions into account

There are 9 letters in the word "tennessee", so without repetitions, the total number of permutations would be 9! (9 factorial).
03

Adjust the result for each letter's repetitions

We need to divide the total number of permutations without repetitions (9!) by the factorial of the number of repetitions for each letter, to adjust for the repetitions: Adjusted permutations = \(\frac{9!}{(4!)(3!)(2!)}\)
04

Calculate the final result

Now, calculate the adjusted permutations: Adjusted permutations = \(\frac{9!}{(4!)(3!)(2!)} = \frac{362880}{(24)(6)(2)} = 15120\) So, there are 15,120 ways to arrange the letters of the word "tennessee".

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