There are nine differently-titled books on a shelf. Four books have red covers, while the other five have black covers. How many different arrangements of the books can there be, if

Question

(a) there are no restrictions on the order in which the books are placed?

Is it 9! ?

(b) all the black-covered books must be together?

Is it 5! ?

(c) all the black-covered books must be together and all the red-covered books must also be together?

is it 2! ?

(d) black- and red-covered books must alternate?

is it 4!5! ?

Answer 1

looks good

Answer 2

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Answer 3

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Answer 4

Yep spot on