Need quick help with these perms/coms questionscheck answers

[rock.freak667]

[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.

Homework Equations

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?

 

[Dick]

Yes to all of the above, I think.

 

[rock.freak667]

well then...great...! I got confused since all of that was 8 marks