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In how many ways can 7 books be arranged on a shelf if

1) there is no restriction

2) 3 particular books always stand together

3) 2 particular books must occupy the ends.

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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