There are 20 students in a class with 7 boys . (a) In how many different ways can a team of 2 boys and 6 girls formed ? (b) In how many different ways can a team of 6 be formed such that there is a least one boy and at least one girl in the team ?
1 Answer
May 13, 2018
a. 36,036 ways
b. 278,460 ways
Explanation:
There are 7 boys and 13 girls in the class.
When picking teams, we're looking at combinations (we don't care in what order the players are picked). The general formula is:
a
We want a team with 2 boys (from a population of 7) and 6 girls (from a population of 13):
b
We want a team of 6 with at least 1 boy and 1 girl. So let's first have 1 guaranteed boy and 1 guaranteed girl:
Now we need to fill in the remaining team. We can pick any of the remaining 18 students to fill in the remaining 4 spots: