## Related questions with answers

Question

Students will be chosen at random for school spirit awards. There are 6 athletes and 8 non-athletes who are eligible for 2 possible prizes. What is each probability? P(no prize is awarded to an athlete)

Solution

VerifiedStep 1

1 of 46 athletes + 8 non-athletes = 14 possible award recipients.

Total number of all possible outcomes for 2 prizes given out:

$\begin{align*} _nC_r &= \dfrac{ n!}{r! (n-r)! } \\\\ _{14}C_2 &= \dfrac{14!}{2! (14-2)! } = \dfrac{ 14! }{ 2(12)! } = \dfrac{ 14(13) }{ 2 } = 7(13) = 91 \end{align*}$

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