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

The total number of choosing p balls out of n balls, without replacement is n! / (p! . (n -p)!) so:

The total number of the times of Choosing 4 red balls out of 5 is C(5 ,4) = 5! / (4! . 1!) = 5

The total number of the times of Choosing 2 orange balls out of 7 is C(7 , 2).= 7! / (2! . 5!) = 21

The total number of choosing 6 balls out of 12 balls is C (12 , 6) = 12! / (6! . 6!) = 924

So the required probability will be 5 . 21 / 924 = .1136... almost 0.114.