You are given nine books and required to put them on a desk. Try to solve the fo

Question

You are given nine books and required to put them on a desk. Try to solve the following problems. Indicate the reason for each of your answer.
(a) If the books are all different, how many distinct ways can you arrange them on the desk?
(b) All the nine books are different and only four of them are selected and put on the desk, how many distinct ways can you arrange the selected books on the desk?
(c) If three among the nine books are identical, how many distinct ways can you arrange the nine books on the desk?
(d) If the nine books consist of three different groups with four alike in the first group, three alike in the second, and two alike in the third, how many distinct ways can you arrange all of the nine books on the desk?

Explanation / Answer

a) 9! = 9x8x7x6x5x4x3x2x1 = 362,880 b) 9x8x7x6 = 3024 c) 6x5x4 = 120 d) 4x3x2 = 24

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