Some years ago, a dancing contest was performed on a small island in the North A

Question

Some years ago, a dancing contest was performed on a small island in the North Atlantic. Six candidates Andy, Beth, Chuck, Di, Eddie, and Fergie presented themselves before Search Committee for interviews. Subsequently, the Committee for warded a short list of throe names to the Judge for his decision. How many different short lists could the Committee have chosen? Assume that all short lists were equally likely to have been chosen, What is the probability that Beth is on the short list? What is the probability that both Beth and Eddie are on the short list?

Explanation / Answer

1. Assume the order on the short list does not matter, the number of short lists is 6C3, i.e. "6 choose 3," which is equal to 20. Out of 6 candidates, we must choose 3. Recall that nCk = n!/(k!*(n-k)!) 2.(a). If Beth is on a short list, the number of lists that can be formed is 5C2 = 10. Thus, the probability that Beth is on a short list is 10/20 = 0.5 2.(b) If both Beth and Eddie are on a short list, the of lists that can be formed is 4C1 = 4. Thus, the probability that both Beth and Eddie are on a short list is 4/20 = 0.2

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.