Balls drawn--8.2

Question

An urn contains 9 white balls and 5 red balls. Four balls are selected. In how many ways can the 4 balls be drawn from the total of 14 balls:

 

a) If 3 balls are white and 1 is red?

b) If all 4 balls are white?

c) If all 4 balls are red?

Answer 1

There are 14 total balls in the urn, and 4 are selected, so there are ₁₄C₄ ways to choose them.

 

a) If you choose 3 out of 9 white, and 1 out of 5 red, there are ₉C₃ and ₅C₁ ways to select them, respectively.

 

₁₄C₄ / (₉C₃ * ₅C₁) is the number of ways to choose 3 white and 1 red ball from this urn.

 

b) You can do the same calculation, with 4 out of 9 white chosen, and 0 out of 5 red.

 

c) Again, the same idea, with 0 out of 9 white, and 4 out of 5 red.