If a choir consists of 2 boys and 3 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.
Options:  A) 120  B) 30  C) 24  D) 11  E) 4
There are 4 possibilities:   bbggg   gbbgg   ggbbg   gggbb   Think of all 2 boys as a single unit. Together with 3 girls it makes a total of 4 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 4 available positions. If the number of available unique positions is 4, then the number of unique patterns equals 4 as well.   Answer: 4.
<result>E</result>
If a choir consists of 2 boys and 3 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.