Question

in how many ways 6books out of 10 different books can be arranged in a bookshelf so that 3particular books are always together​

Answer 1

This is a problem on permutations and combinations.First of all, let us choose 6 books out of 10 books. This can be done in 10C6 = 10 C4= 10.9.8.7/4.3.2.1=210 ways.Now, the 6 books so chosen have to kept on a bookshelf so that three of these 6 books are together. Take these 3 books as one book say B.Then this B with other 3 form 4 books. They can be arranged in 4! =24 ways. Three books in B can be arranged among themselves in 3! = 6 ways.Hence the total number of ways of choosing 6 books from out of 10 books so that three particular books are always together is, by fundamental counting principle, 210x24x6 = 30240 ways.

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Answer 2

Answer:

in how many ways 6books out of 10 different books can be arranged in a bookshelf so that 3particular books are always together