Twenty-one boys and eight girls go on a camping trip. In how many ways can a group of six be selected to gather firewood, given the following conditions?

(a) The group consists of two girls and four boys.

(b) The group contains at least two girls.

(a) there are 8C2 = 28 ways of picking 2 girls from 8

And there are 21C4 = 5985 ways of picking 4 boys

Required number of ways for 2g / 4b = 28 * 5985 = 167,580

(b) at least 2 girls means combinations of 2g/4b, 3g, 3b, 4g/2b, 5g 1b or

6 girls.

2g/4b = 167,580 ways

3g/3b = 8C3 * 21C3 = 56 * 1330 = 74,480

4g/2b = 8C4 * 21C2 = 70 * 210 = 14,700

5g 1b = 8C5 * 21 = 56*21 = 1176

6 girls = 8C6 = 28

adding these up we get the answer to (b) which is 257,964