Answer to Question #293110 in Statistics and Probability for Ann

Question

A box contains 6 red balls, 5 blue balls, and 10 green bas. In how many ways can you choose 2 red balls and 5 green balls

Answer 1

There are,  6 red balls, 5 blue balls, and 10 green balls.

The number of ways to choose 2 red balls out of 6 red balls is, $\binom{6}{2}={6\times 5\over 2}=15$

The number of ways to choose 5 green balls out of 10 green balls is, $\binom{10}{5}={10\times 9\times 8\times 7\times 6\over 5\times4\times 3\times2}=252$

Therefore, the number of ways to choose  2 red balls and 5 green balls is $15\times252=3780$ ways.