Probability of random occurrence

Question

Three members from each team's twenty player hockey team roster are randomly selected for drug testing at the beginning of a tournament. The coach of a low-seeded team complains when none of the starters from the #1 seeded team were selected for testing. What is the probability that this occurred randomly?

Answer 1

The total number of ways of choosing 3 of the 20 players is N=C(20,3) where C(n,r)=(n!)/[(r!)(n-r)!] i.e the number of combinations of choosing 3 out of 20.

 

Assuming five players are designated as starters then all three were chosen from the remaining 15. That would be  N_A=C(15,3).

 

The probability would be N_A/N.

 

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