Question

The Club has 9 members. The club needs to elect a President, Vice President, Secretary and Treasurer, how many different ways are possible? How many ways are there to find a committee of size three.

The Club has 10 members, 3 freshman, 4 sophomores and 3 juniors. How many ways are there to find a committee of size three with no freshmen? How many ways are there to find a committee of size three with one freshmen?

Answer 1

Permutations Formula

:

Combinations Formula

Number of members in the club = 9

Number of positions = 4 (President, Vice President, Secretary and Treasurer)

This is the case of the number of "different" ways to select 4 items out of 9. where the order matters (who holds the president matters) and no repetition is allowed.

Number of  many different ways that are possible =

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Number of members in the club = 9

Size of the committee = 3

This is the case of the number of "different" ways to select 4 items out of 9. where the order does not matter and no repetition is allowed.

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The Club has 10 members, 3 freshman, 4 sophomores and 3 juniors. How many ways are there to find a committee of size three with no freshmen?

Total number of members = 10

Committee size = 3

Total number of members with no freshmen = Total number of members - Number of freshmen =10-3 =7

Number of ways to select a committee of size three with no freshmen = Number of ways of selecting 3 members from the 7 members (with no freshmen)

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Total number of members = 10

Committee size = 3

Total number of members with one freshmen =

Number of ways to find a committee of size three with one freshmen

= number of ways of selecting one freshman from 3 freshmen x Number ways of selecting remaining 2 members from the 7 members (with no freshmen)

Number of ways to find a committee of size three with one freshmen = 63