In how many ways can 7 books be arranged on a shelf if 3 particular books always stand together

Dear Student, 
1) If there is no restriction then the total arrangements is given by 7!= 5040 . 
2)If three Particular books are to be together we make one packet of those three books, and thus the packet along with remaining 4 books can be arranged in 5! ways= 120 , and within the packet the three books can be arranged in 3!=6 ways 
so total number of such arrangements= 120x6= 720 
3) If 2 particular books to occupy end places, this can happen in 2! ways=2 ways, then rest of the 5 books can be arranged in 5! ways=120 ways, so total number of such arrangements are 2x120=240 ways 
Hope this clears your doubt 
With regards 


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In how many ways can 7 books be arranged on a shelf if 3 particular books always stand together

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Updated On: 27-06-2022

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In how many ways can 7 books be arranged on a shelf if 3 particular books always stand together

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How many ways can 7 books be arranged on a shelf if 1/3 particular books always stand together ii two particular books must occupy the?

So there are 5040 ways to arrange 7 books on a shelf.

How many different orders can 7 books be arranged on a shelf if a certain 3 volume book is not to be separated?

If a certain 3 volume work is not to be separated, will be 3 factorial times 5 factorial, and that is 720 repoint.

How many ways can 7 books be arranged on a shelf in groups of 5?

Summary: 7 books can be arranged on a shelf 5 at a time in 2520 ways.

How many ways can 8 books be arranged on a shelf if 3 particular books are to be together?

Hence the number of ways can 8 books be arranged on a shelf if 3 particular books must always stand together are 4320.