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Chapter 11: Problem 65

I used the Fundamental Counting Principle to determine the number of permutations of the letters of the word ENGLISH.

Short Answer

Expert verified
The number of permutations of the word 'ENGLISH' is 5040

Step by step solution

01

Identify the Number of Elements

For this problem, we are looking at the word 'ENGLISH', which has 7 letters, each of them different. So, we have 7 elements to arrange.
02

Apply the Fundamental Counting Principle

Assuming all characters are distinct, the Fundamental Counting Principle is used to determine the number of ways these can be arranged. It states that if there are n different things to be arranged, there are n factorial (n!) ways to arrange them. Hence, for the 7 distinct letters, there are 7 factorial (7!) ways.
03

Calculate the Value

To determine the numerical solution, we need to calculate the factorial of 7 . This is done as follows: \(7! = 7*6*5*4*3*2*1 = 5040\).

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