Question

A bag contains 6 red balls and blue balls. 4 balls are selected at random. find the probability of selecting 4 red balls.

Answer 1

Another way is to note that there are (104)(104) (“10 choose 4”) ways to select 4 balls from a collection of 10. If 4 of those 10 balls are “special” in some way (in this case, “special” = “red”), then the number of ways to choose 4 special balls is (44)(44). (The factor of (60)(60) is included to convey that, after choosing 4 special balls, we choose none of the 6 non-special balls.) This line of reasoning gives the second expression.