Question

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

Answer 1

Let the books be represented by letters A to G.

If the particular books that need to be together are A, B and C, then we can consider them as a single unit, which we can call H. So we have D, E, F, G and H. That is 5 different entities which can be arranged in 120 different ways. However, the three selected books can be arranged in 6 ways and still be together. The total number of ways is 6×120=720 ways.