Combination, partial permutation

[Memo]

Homework Statement

A pet store has 10 cats (4 of which are of the Maine Coon breed) waiting to be sold. A person buys 3 cats
a) find the proportion that 1 Maine Coon is bought.
b) find the proportion that at least 1 Maine Coon is bought.

Relevant Equations

nCr=n!/(r!*(n-r)!)

a) p=(4C1*6C2)/(10C3)=0.5
b) p=(4C1*6C2)/(10C3) + (4C2*6C1)/(10C3) + (4C3*6C0)/(10C3)=0.83
Please check if my answer is correct. Thank you very much.

 

[PeroK]

I guess the question is that someone buys three cats at random, with each cat equally likely to be chosen. (That's an unusual way to buy pets!) And to find the probability that a) 1 and b) at least one Maine Coon is bought?

You should try to find a way to check the answer yourself - such as doing the problem two different ways and checking you get the same answer.

For b), you could calculate the probability that no Maine Coons cats are bought. Then the probability that at least one is bought is tyhe complement of this.

That said, both answers are correct.