Question

In how many ways can 6 books be arranged on a shelf?

Answer 1

This question is from the topic of permutation and combination. In this question, we will find the number of ways of arranging 6 books on a shelf. In solving this question, we will first understand how to find the number of ways of arranging n elements. After solving the further question, we will get our answer.

Complete step-by-step answer:
Let us solve this question.
In this question, we have asked to find the number of arrangements of books on a shelf. It is given that the number of books is 6.
So, let us first understand how to find the number of ways of arrangements.
We can say that if there is 1 element, then there will only be one arrangement for 1 element that is n=1!=1.
Similarly, if there are 2 elements, then the arrangements will be n=2! =2
If there are 3 elements, the number of ways of arranging will be n=3! =6
If there are 4 elements, the number of ways of arranging will be n=4! =24
So, we can say that if there are n elements or n objects, then the number of ways of arranging them will be n!.
Hence, for arranging 6 books on a shelf, the number of ways will be 6! = 720

Note: We should have a better knowledge in the topic of permutation and combination to solve this type of question easily. We should know the formula of n!. Remember the following formula:
$n!=n\times \left( n-1 \right)\times \left( n-2 \right)\times ..........3\times 2\times 1$
As we can see that it is not given in the question that same or different, so if the books are the same, then the number of ways of arrangement will always be 1.
And, if the number of books are different, then the number of ways of arrangement will always be n!, where n is the number of books.