There are 9 white balls and 4 red balls in an urn How many d

There are 9 white balls and 4 red balls in an urn. How many different ways are there to select a subset of 6 balls, assuming the 13 balls are different?

What is the fraction of selections with 4 whites and 2 reds?

Solution

a) to select a subset of 6 balls, assuming the 13 balls are different

9C6 x 4C0+9C5 x 4C1+9C4 x 4C2+9C3 x 4C3+9C2 x 4C4=84+504+756+336+36=1776

ways to select a subset of 6 balls from 9 white balls and 4 red balls in an urn

b)fraction of selections with 4 whites and 2 reds

(9C4 x 4C2)/13C6=756/1716