# Working with some identical objects using permutations and combinations.

Wing has different books to arrange on a shelf: 4 blue, 3 green, and 2 red.

(a) In how many ways can the books be arranged on a shelf?

(b) If books of the same color are to be grouped together, how many arrangements are possible?

(c) In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together?

(d) In how many ways can you select 3 books, one of each color, if the order in which the books are selected does not matter?

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#### Solution Preview

Suppose C(n,m)=n!/(m!*(n-m)!), P(n,m)=n!/(n-m)!

(a) We have 9 positions. We first choose 4 positions for 4 blue books and permutate them, then choose 3 positions in the rest 5 positions for 3 green ones and permutate, then put 2 red ...

#### Solution Summary

Permutations and combinations are analyzed with regard to whether order of objects has importance.