A sports team has 7 players. In how many ways can the team select a captain and junior captain?

Jason Farmer

Jason Farmer

Answered question

2020-12-05

A sports team has 7 players. In how many ways can the team select a captain and junior captain?

Answer & Explanation

okomgcae

okomgcae

Skilled2020-12-06Added 93 answers

Definition permutation (order is important): P(n,r)=n!nr!
Definition combination (order is not important):
C(n,r)=(nr)=n!r!(nr)!
with nn(n1)21.
We are interested in selecting two of the seven players.
n=7
r=2
The order of the players is important (as a diffirent order results in a diffirent captain and junior captain), thus we need to use the definition or permutation.
Evaluate the definition of permutation at n=7 and r=2:
7P2=7!727!5765!576=42

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