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Chapter 9: Problem 27

In how many ways can five children posing for a photograph line up in a row?

Short Answer

Expert verified
The five children can be arranged in 120 different ways for the photograph.

Step by step solution

01

Understand the problem

There are five children, each unique, they can stand in any order. So, we need to find the number of ways they can line up.
02

Use the permutation formula

The problem can be solved by using permutation formula, \(\text{nPr} = \frac{n!}{(n-r)!}\), where \(n\) is total number of items, \(r\) is the number of items to choose and the symbol '!' denotes factorial. Here both \(n\) and \(r\) are 5, since 5 kids are to be arranged in a row.
03

Calculate factorial

Now, based on formula put the values into it, which results to \(\text{5P5} = \frac{5!}{(5-5)!}\). Factorial, represented with the symbol '!', is the product of all positive integers less than or equal to that number. The factorial of 5 is \(5*4*3*2*1 = 120\) and factorial of 0 is 1. So, \(\frac{5!}{0!} = 120/1\).

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Most popular questions from this chapter

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