ISEE Word Problems Question 232: Answer and Explanation
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Question: 232
12. The 5-member pep squad plans to send 2 of its members to the debate contest. How many combinations of 2 members are possible from the 5-member squad?
- A. 20
- B. 10
- C. 5
- D. 2
Correct Answer: B
Explanation:
The answer is B
The number of combinations possible when r are selected from n options is given by 
. Here, the number of combinations is 
= 10.
When dealing with orderings or combinations, you can set up slots for what you need and fill them with what is available. In this case we need two people, so we need two slots: ____ ____. For the first slot, 5 people are available as a possible choice, while for the second slot only 4 people are available (as one is taken for the first slot): 5 4 . If we wanted to know how many orderings there are, we would multiply the numbers in the slots, in this case 20. However, this would double count the number of groups because AB and BA are the same. Thus, we need to cut 20 in half.