# Need quick help with these perms/coms questionscheck answers

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[SOLVED] Need quick help with these perms/coms questions..check answers

## Homework Statement

A cricket selection committee of 4 members is to be chosen from 5 former batsmen and 3 former bowlers.

In how many ways can this committee be selected so that the committee includes at least

1)One former batsman
2) One batsman and one bowler.

## The Attempt at a Solution

B=Batsman
b=bowlers

1)At least one former batsman

1B 3b=5C1*3C3=5
2B 2b=5C2*3C2=30
3B 1b=5C3*3C1=30
4B 0b=5C4=5

total=70 ways

2) no. of way to select without any restriction=8C4=70

so for at least one B and one b, it is 70-5=65

Also,since in part 1,those are the only ways to make the selection.....does that mean I could have just said 8C4 instead of writing out all the ways?

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