permutatiions

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

bbbbbgggggg
gbbbbbggggg
ggbbbbbgggg
gggbbbbbggg
ggggbbbbbgg
gggggbbbbbg
ggggggbbbbb

7.

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.