Question

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

Answer 1

This question is from the topic of permutation and combination. In this question, we will find the number of ways in which 5 children can line up in a row. In solving this question, we will first understand how many ways there can be if the number of children is n. After that, we will find the ways to line up in a row for five children.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to find the number of ways for which the five children can stand up in a row.
So, let us first know that if there was only one child, then the number of ways of standing in a row will be 1 or we can say 1!.
If there were two children, then the number of ways of standing in a row will be 2 or we can say 2!.
If there were three children, then the number of ways of standing in a row will be 6 or we can say 3!.
So, we can say that if there were n children, then the number of ways of n children to line up in a row will be n!.

Hence, the number of ways of 5 children to line up in a row will be 5! which can also be written as
$5!=5\times 4\times 3\times 2\times 1=120$

Note: We should have a better knowledge in the topic of permutation and combination to solve this type of question easily. Remember that if we have to arrange or line up n different things or n people, then for arranging or lining up, the number of ways will be n!. We should have a better knowledge in the topic of binomial theorem also. We should know the following formulas:
$0!=1$
$1!=1$
$n!=n\times \left( n-1 \right)\times \left( n-2 \right)\times \left( n-3 \right)\times ...........\times 4\times 3\times 2\times 1$