SOLUTION: The offices of president, vice-president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the d

Question 1100877: The offices of president, vice-president, secretary, and treasurer for an environmental club will be filled from a pool of 14 candidates. Six of the candidates are members of the debate team. What is the probability that exactly 2 of the members of the debate team will be chosen for one of the four offices?
Found 2 solutions by greenestamps, richwmiller:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For the exact question that you asked, the probability is zero, because it is impossible for ANY two people to be chosen for one office.

I assume, then, that what you really meant to ask is the probability that members of the debate team are chosen for 2 of the 4 offices.

In that case, you are choosing 4 of the 14 to be officers; and they must include 2 of the 6 members of the debate tean and 2 of the 8 others. The probability is then

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
For the exact question that you asked, the probability is zero, because it is impossible for ANY two people to be chosen for one office.
I have wondered about that possibility.
Perhaps two people to fill one position. It does happen. Not in elections, as far as I know, but by appointment. How would you figure that rarity into probability or wouldn't you since it is not one of the original possibilities?
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