Probabilities of draws without replacement

Question

An urn contains 5 red balls and 7 orange balls. If Tim chooses 6 balls at random from the urn, what is the probability that he will select 4 red balls and 2 orange balls? Round your answer to 3 decimal places.

Answer 1

There are a total of 12 balls (5 red and 7 orange balls) in the box. We will select 6 balls at random. We will use the probability with combinations.

1.) How many ways to select 6 balls at random? C(12, 6) = 12! / (6!)*(6!) = 924

2.) How many ways to select 4 red balls? C(5, 4) = 5! / (4!)*(1!) = 5

3.) How many ways to select 2 orange balls? C(7, 2) = 7! / (2!)*(5!) = 21

P(4 red and 2 orange balls) = (5*21) / 924 = 105/924 ≈ 0.114

The probability that Tim will select 4 red balls and 2 orange balls is about 0.114.