A classroom of children has 11 boys and 20 girls in which five students are chos

Question

A classroom of children has 11 boys and 20 girls in which five students are chosen to do presentations. In how many ways can the five students be chosen so that more boys than girls are selected?

A committee consists of 8 men and 14 women. In how many ways can a subcommittee of 3 men and 7 women be chosen?

A business organization needs to make up a 6 member fund-raising committee. The organization has 10 accounting majors and 7 finance majors. In how many ways can the fund-raising committee be formed if at most 1 accounting major is on the committee?

Explanation / Answer

1. There are 11 boys and 20 girls.

Number of ways to choose five boys = 11C5.

Number of ways to choose four boys and one girl = 11C4 * 20C1.

Number of ways to choose three boys and two girls = 11C3 * 20C2.

=> Total number of ways to choose more boys than girls = 11C5 + 11C4 * 20C1 + 11C3 * 20C2

= 462 + 6600 + 31350

= 38412.

2. There are 8 men and 14 women.

The 3 men can be chosen in 8C3 ways and the 7 women in 14C7 ways.

=> Total number of subcommittees = 8C3 * 14C7 = 56 * 3432 = 192192.

3. There are 10 accounting majors and 7 finance majors.

Number of ways to choose 6 finance majors = 7C6.

Number of ways to choose 5 finance majors and one accounting major = 7C5 * 10C1.

=> Total number of ways can the fund-raising committee be formed if at most 1 accounting major is on the committee = 7C6 + 7C5 * 10C1

= 7 + 210

= 217.

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