Answer to Question #47151 in Statistics and Probability for irebami

Question

In how many ways can a committee of 5 people be chosen out of 9 poeple?

254
126
120
131

Answer 1

If we distinguish people of a committee (for example, chair, secretary and so on), then the first person of committee can be chosen in 9 ways, the second person in 8 ways, the third person in 7 ways, the fourth person in 6 ways, the fifth person in 5 ways. By multiplication rule, a committee of 5 people out of 9 people can be chosen in 9*8*7*6*5=3024 ways. If we do not distinguish people of a committee, then a committee of 5 people out of 9 people can be chosen in 9!/(4!*5!)=126 ways.