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In how many ways can 7 different books be arranged in a shelf ? in how many ways can we arrange three particular books so that they are always together?

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by ikshugandha

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by ikshugandha

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

2) If 3 particular books must always stand together, the 3 books can occupy the following positions on the shelf:

BBB----

-BBB---

--BBB--

---BBB-

----BBB

For each of these five cases, there are 3! permutations of the 3 books and 4! permutations of the other 4 books,

so the total number of allowed arrangements is 5 x 3!4! = 720.

Consider 3 particular books as 1 unit

1 unit +remaining 4 books=5

these 5 can be placed in120 ways

1 unit +remaining 4 books=5

these 5 can be placed in