If a choir consists of 2 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. Choose one.
A) 120 B) 30 C) 24 D) 8 E) 17
There are 8 possibilities:   bbggggggg   gbbgggggg   ggbbggggg   gggbbgggg   ggggbbggg   gggggbbgg   ggggggbbg   gggggggbb   Think of all 2 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>D</result>
If a choir consists of 2 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.