Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, four white ones, and three purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms.

Question

Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, three green ones, four white ones, and three purple ones. She grabs seven of them. Find the probability of the following event, expressing it as a fraction in lowest terms.
She has all the red ones.
 
So it should be that n(s)=c(13,7)=? I don't know how to get the answer to what that is equal to and also after that, it should be n(e)=c(3,3)*c(7,4)=?

Reiny · Answer

You are partly on the right track.
The C(13,7) is the number of to choose 7 of the 13 marbles.
you want the case of 3 reds plus 4 non-reds

prob(your stated event) = C(3,3)*C(10,4)/C(13,7)
= 1*210/1716
= 35/286