Answer to Question #238970 in Statistics and Probability for chan

Question

A bag contains seven white marbles and five black marbles. Find the number of ways four marbles can be drawn from the bag if

a) they can be of either color

b) two must be white and two black. 

Answer 1

Seven white + five black = Total 12

a) The number of ways to select 4 marbles $= \frac{12!}{4!(12-4)!} = \frac{11880}{24}=495$

b) The number of ways to select 2 white and 2 black $= \frac{7!}{2!(7-2)!} \times \frac{5!}{2!(5-2)!}$

$= 21 \times 10 = 210$