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Please Solve Correctly ASAP. A class consist of 55 students, 20 are juniors, 5 are seniors,...

Please Solve Correctly ASAP.

A class consist of 55 students,

20 are juniors, 5 are seniors, and 15 are sophomore freshman

5 are to be selected as president, vice president, treasure, secretary and minister.

Find the probability that the five selected are

  1. All Seniors
  2. All juniors
math   Statistics-And-Probability   
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Answer #1

\\ Number \ of\ Junior=20\\ Number\ of\ Senior=5\\ Number\ of\ Sophomore=15\\ Number\ of\ Freshman=15\\ \\ Total\ member =55\\ \\ \\ Number\ of\ way \ to\ select\ 5\ member = \binom{55}5=\frac{55!}{50!5!}=3478761\\ \\ \\ i)\ Number\ of\ way\ to\ select\ all\ seniors = \binom{5}{5}=1\\ \\ So, \ probability =\frac{1}{3478761}=2.8745\times 10^{-7}=\frac{1}{^{55}C_5}\\ \\ \\ ii)\ Number\ of\ way\ to\ select\ all\ Juniors =\binom{20}{5}=\frac{20!}{15!5!}=15504\\ \\ So,\ probability =\frac{15504}{3478761}=0.004567=\frac{^{20}C_5}{^{55}C_5}

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