Question

You have 9 black balloons, 5 white balloons, 4 brown balloons, and 2 purple balloons. You randomly select 4 without replacement, the order doesn't matter.

What is the probability that 1 each of every color is drawn?

Answer 1

Solution:

Given: There are

9 black balloons,

5 white balloons,

4 brown balloons, and

2 purple balloons.

Total =20

4 balloons are randomly selected without replacement.

We have to find:

P( 1 Black , 1 White, 1 Brown , 1 Purple) =...........?

P( 1 Black , 1 White, 1 Brown , 1 Purple) = ₉C₁ X ₅C₁ X ₄C₁ X ₂C₁ / ₂₀C₄

Thus

P( 1 Black , 1 White, 1 Brown , 1 Purple) = ₉C₁ X ₅C₁ X ₄C₁ X ₂C₁ / ₂₀C₄

P( 1 Black , 1 White, 1 Brown , 1 Purple) = 9 X 5 X 4 x 2 / 4845

P( 1 Black , 1 White, 1 Brown , 1 Purple) = 360 /4845

P( 1 Black , 1 White, 1 Brown , 1 Purple) = 0.074303