stats binomial coefficient problem?

Question

a committee of 4 men is to be chosen from 7 men, 2 of whome are brothers
Find
a) P(that the brothers will be in committee)

b) P(at least one brother will be in committee)

c) P(neither brother will be in committee)

MUST use combinations or binomial coefficient nCr

how did u get the 9
there're only 7 ppl and two of them are brothers. if this is the case then it should be like 7C4 which is the total.
right

Answer 1

Total no of ways of choosing 4 from 7 is 7C4.

Now let's suppose both brothers are in. This is the same as choosing 2 out of 2 AND 2 out of hte remaining 5.
no of ways = 2C2 * 5C2.
Prob = 2C2 * 5C2 / 7C4 = 2/7

If only one brother is in, then you're choosing 1 out of 2 and 3 out of 5.
no of ways = 2C1 * 5C3.
Prob = 2C1 * 5C3 / 7C4 = 4/7
Prob of at least one = 6/7. Just add them.

If no brothers are in, then you're choosing 4 from 5.
no of ways = 5C4.
Prob = 5C4 / 7C4 = 1/7

Can you verify that the probs add up to 1. Be careful which ones you add.

Answer 2

Total possible combinations is 9C4
a)
(7C2)/(9C4)
b)
2(7C3)/(9C4)
c)
(7C4)/(9C4)