Homework Answers
4 RED, 3 BLUE, 6 GREEN, 5 YELLOW books
Total number of books= 18
Total number of possible arrangements of books on a shelf= 18!
About the books, imagine that that the RED books are placed in a box, labelled R. BLUE books are also placed in a box, labelled B GREEN books are placed in a box, labelled G and YELLOW books are placed in a box, labelled Y.Then we have 4 objects, that is the 4 boxs R, B, G,and Y. These can be arranged on the shelf in 4! ways. For each of these ways, the RED books can be taken out of the box and arranged in 4! ways, the BLUE books can be taken out of the box and arranged in 3! ways,the GREEN books can be taken out of the box and arranged in 6! ways, the YELLOW books can be taken out of the box and arranged in 5! ways, .
thus the total number of ways for the books of same colour to be together is 4!.4!.3!.6!.5!
Thus the probability that all books of the same colour are placed next to each other=( 4!.4!.3!.6!.5! )/ 18!
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