in how many ways can 10 books be arranged on a shelf so that a particular pair of books shall never be together
Answers
Answer:
Ans= 9!×8
Step-by-step explanation:
Total number of ways in which we can arrange 10 books on a shelf
= 10P10 =10! (A)
Now we will find out total number of ways in which 10 books can be arranged on a shelf such that a particular pair of books will always be together.
We have a total of 10 books. If a particular pair of books must always be together, just tie these two books together and consider as a single book. Hence we can take total number of books as 9. These 9 books can be arranged in 9P9 =9! ways.
We had tied two books together. These books can be arranged among themselves in 2P2 =2! ways.
Hence, total number of ways in which 10 books can be arranged on a shelf such that a particular pair of books will always be together
=9!×2! (B)
From (A) and (B),
Total number of ways in which 10 books can be arranged on a shelf such that a particular pair of books will never be together
=10!-(9!×2!)= 10!-(9!×2)= (9!×10)-(9!×2)= 9!(10-2)=9!×8
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