SOLUTION: A debate club consists of 12 men and 10 women. a) In how many ways can the club select a president, vice president and treasurer? (Assume no person can hold two offices at once) b)

Question 326552: A debate club consists of 12 men and 10 women. a) In how many ways can the club select a president, vice president and treasurer? (Assume no person can hold two offices at once) b) In how many ways can the club select a president, vice president and treasurer where all three officers are male? c) What is the probability that all three officers are male? d) What is the probability of selecting at least one female officer?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A debate club consists of 12 men and 10 women.
a) In how many ways can the club select a president, vice president and treasurer? (Assume no person can hold two offices at once)
Ans: 32*31*30
==============================
b) In how many ways can the club select a president, vice president and treasurer where all three officers are male?
Ans: 12*11*10
==============================
c) What is the probability that all three officers are male?
Ams" 12C3/22C3 = (12*11*10)/(1*2*3) = 220
==============================
d) What is the probability of selecting at least one female officer?
P(at least one) = 1 - P(none)
---
P(at least one female) = 1 - P(3 men) = 1 - [12C3/22C3]
= 0.8571
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Cheers,
Stan H.
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