Question

Suppose there is a deck where every card has both a single color and a single number. Suppose the colors are Red, Green, and Blue and the numbers are 1-20.

How many ways are there to choose 5 blue cards from this deck?
What is the probability that five randomly chosen cards will all be colored blue?
What is the probability that five randomly chosen cards will all show the number 8?

Answer 1

For the first question there are 20 blue cards and you are taking 5 of them.

So, use "20 choose 5" which equals 15504 different ways that you can pull out 5 cards from 20.

For the second question, you first have to see that there are 60 cards in total and 20 are blue.

The first card will have a 20/60 or 1/3 probability. For any further drawings, though, there will be less cards.

Probability: (1/3)x(19/59)x(18/58)x(17/57)x(16/56)=0.0028 or 0.28% approx.

For the third problem it is the same idea. But it is not possible because there are only 3 cards that have the number 8 and you need to draw 5 cards.

Probability: 0%