alphabeta1234 wrote:
A committee of three people is to be chosen from four teams of two. What is the number of different committees that can be chosen if no two people from the same team can be selected for the committee?
A. 20
B. 22
C. 26
D. 30
E. 32
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Solution:There are 8 options for the first member, 6 options for the second member (since the first member and his/her teammate cannot be selected) and 4 options for the third member.
If the order were important (for instance, if we were selecting a president, a vice president and a secretary); there would be 8 x 6 x 4 options. However, as the order is not important, there are (8 x 6 x 4)/3! = 8 x 4 = 32 possible selections.
Alternate Solution:First, let’s select three teams out of four. Since there are four teams and we are selecting three, this can be done in 4 ways (just choose one team which is not to be selected).
Next, out of the three teams we pick, we have two options for each team (the first member or the second member). Thus, there are in total 4 x 2 x 2 x 2 = 32 possible selections.
Answer: E _________________
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