Bunuel wrote:
Official Solution:
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.
A. 120
B. 30
C. 24
D. 11
E. 7
There are 7 possibilities:
bbbbbgggggg
gbbbbbggggg
ggbbbbbgggg
gggbbbbbggg
ggggbbbbbgg
gggggbbbbbg
ggggggbbbbb
Formally, \(\frac{7!}{6!} = 7\).
Alternative explanation:
Think of all 5 boys as a single unit. Together with 6 girls it makes a total of 7 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 7 available positions. If the number of available unique positions is 7, then the number of unique patterns equals 7 as well.
Answer: E
Hi Bunnel
What do we mean by the following statement-
Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
Do we mean to say that we need to ignore the {5!} and {6!} ways in which the boys and girls can be arranged among themselves....??
This is what I understood.Please clarify.
Thanks
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