Statistics HW (help please)

[Menasor2]

I know this question on my hw might seem easy or is but I can't for the life of me get it.

Suppose there are 55 democrats and 45 republicans in the US senate. A committee of 7 senators is to be formed by selecting members of the senate randomly.

a. what is the probability that the committee is composed of all democrats?

b. what is the probability that the committee is composed of all republicans?

c. what is the probability that the committee is composed of 4 democrats and three republicans?


I have all my notes but do not understand how to set this up. I'm sure it uses the formula nCr on the calculator or even nPr. Anyone good at stats?

[MGS2392]

nCr is the "combination" function. Out of n objects, you find the number of combinations involving choosing r objects, with order not mattering. nPr is the "permutation" function. That's like the combination function, except order matters (for example, when rolling a dice, 5-6 would be treated differently from 6-5).

a. There's 55c7 ways of picking all Democrats. There's 100c7 ways of choosing 7 senators. Therefore, the probability is (55c7)/(100c7).
b. Similar methodology to the above.
c. Not sure about this one.

[DexterMorgan]

Try doing it for a committe of two members, questions A and B same as above, and for c. try probability of 1 dem and 1 repub.