From a group of 7 candidates, a committee of 6 people is selected. In how many different ways can the committee be selected

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Borys Shumyatskiy eNotes educator| Certified Educator


If all of committee members have equal rights, then to select 6 people from 7 candidates is the same as to select ONE people who is NOT in the committee. There are 7 ways to select one people, so there are 7 ways to select a committee. Also it is known as the number of combinations from 7 by 6, `C_7^6=C_7^1.` 

If, for example, a committee has 1 chairman, then there are 7 ways for selecting a chairman and 6 ways to select a man not in a committee, 7*6=42 ways at all.

The answer for the simple question is 7 ways.