Question

A case of 24 vegetable cans has 1 that is contaminated. 3 cans are to be chosen at random for testing.

a. How many different combinations of 3 cans are there?
b. What is the probability that the contaminated can is selected for testing with any given set of 3 cans?

Answer 1

How many ways can we pick 3 thing out of a field of 24 if the order does not matter. 24C3 means 24 x 23 x 22 divided by 3 x 2 x 1 or 6


24 x 23 x 22
3! (3 x 2 x 1)

12,144 /6 = 2,024 combinations of 3 cans.

The probability that you have the contaminated can in any of those 3 can combinations is 1 in 2,024 or 1/,024