How many ways can we choose three items at random without replacement from five items (A, B, C, D, E) if the order of the selected items is not important?
A)60
B)120
C)10
D)24

Question

Quizplus · Accepted Answer

The number of combinations of choosing three items out of five is given by 5 choose 3 which is equal to (5!)/(3!(5-3)!) = 10. Since the order of the selected items is not important, we do not need to consider permutations which would have been necessary if the order was important. Therefore, the answer is 10 or choice letter C.

How Many Ways Can We Choose Three Items at Random