If a choir consists of 5 boys and 7 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.  Answers: A) 120 B) 30 C) 24 D) 11 E) 8
There are 7 possibilities:   bbbbbggggggg   gbbbbbgggggg   ggbbbbbggggg   gggbbbbbgggg   ggggbbbbbggg   gggggbbbbbgg   ggggggbbbbbg   gggggggbbbbb   Think of all 5 boys as a single unit. Together with 7 girls it makes a total of 8 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 8 available positions. If the number of available unique positions is 8, then the number of unique patterns equals 8 as well.   Answer: 8.
<result>E</result>
If a choir consists of 5 boys and 7 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.