A committee of 5 people is chosen from 6 men and 4 women. in how many ways can this be done
1) if there must be more men than women on the commitee.
2) if there must be 3 men and 2 women, and one particular woman refuses to be on the commitee with one particular man

Question

A committee of 5 people is chosen from 6 men and 4 women. in how many ways can this be done 
1) if there must be more men than women on the commitee.
2) if there must be 3 men and 2 women, and one particular woman refuses to be on the commitee with one particular man

anonymous · Answer

Permutations and combinations....

anonymous · Answer

More men is when
No. of men is 3 or No. of men is 4 or No. of men is 5

anonymous · Answer

Which means there must be atleast three men

anonymous · Answer

6C3*7C2
First we choose at least three 3 men then choose any two people from the remaining people

anonymous · Answer

got it?

anonymous · Answer

the answer is 186

anonymous · Answer

the marking scheme says choose 4 men and 1 women or 5 men and no women. i don't understand why we can't choose 3 men and 2 women.

anonymous · Answer

u can do it too

anonymous · Answer

I mean u can choose 3 men and 2 women

anonymous · Answer

yeah but i wonder why in my mark scheme it's not given. that's why the total answer is 186 but i got 180. by choosing 4 men, 1 women and 3 men 2 women. thanks anyways..:)

anonymous · Answer

do you know how to do the second part?

anonymous · Answer

6C3 * 4C2 + 6C4 *4C1 +6C5 =120+60+6=186

anonymous · Answer

U forgot the case when all are men

anonymous · Answer

Can someone tell me why 6C3 *7C2 doest work

shubhamsrg · Answer

I was also wondering the same thing.

hmm..

shubhamsrg · Answer

M1 M2 M3 M4 M5 M6 W1 W2 W3 W4


Can we try to rationalize ?

anonymous · Answer

@sauravshakya, can you explain how u got 6C3*7C2 ?

anonymous · Answer

First we choose at least three 3 men then choose any two people from the remaining people