rtaha2412 wrote:If a choir consists of 5 boys and 6 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
120
30
24
11
7
Since the boys have to be together, we can think of them as a single element: B.
Since the 6 girls do not have to be together, we must represent them as separate elements: gggggg.
Thus, we need to count the number of ways to arrange the 7 elements Bgggggg.
The number of ways to arrange 7 elements = 7!.
But since we have 6 of the same element -- the 6 g's -- the number of unique arrangements will be smaller. To account for the repeated element, we need to divide by (number of repetitions)!. Since we have 6 g's, we have to divide by 6!.
Thus, the number of possible arrangements is 7!/6! = 7.
The correct answer is
E.
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