The math club at a certain school has 10 members, of which 6 are seniors and 4 juniors. In how many ways can they form a group of 5 members to go to a tournament, if at least 4 of them have to be seniors (aka either a group of 4 seniors and 1 junior, or a group of 5 seniors

Question

Roderick

Mathematics

6 February, 05:26

The math club at a certain school has 10 members, of which 6 are seniors and 4 juniors. In how many ways can they form a group of 5 members to go to a tournament, if at least 4 of them have to be seniors (aka either a group of 4 seniors and 1 junior, or a group of 5 seniors

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Answers (1)

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Goose · Answer 1

Answer: 66 ways

Step-by-step explanation:

Given;

Number of senior math club members = 6

Number of junior math club members = 4

Total number of members of the club = 10

To form a group of 5 members with at least 4 seniors.

N = Na + Nb

Na = number of possible ways of selecting 4 seniors and 1 junior

Nb = number of possible ways of selecting 5 seniors.

Since the selection is does not involve ranks (order is not important)

Na = 6C4 * 4C1 = 6!/4!2! * 4!/3!1! = 15 * 4 = 60

Nb = 6C5 = 6!/5!1! = 6

N = Na + Nb = 60+6

N = 66 ways