ISEE Word Problems Question 268: Answer and Explanation

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Question: 268

2. From a club of 7 members, 3 will be chosen for President, Vice President, and Treasurer. How many different arrangements of members are possible for the 3 positions?

  • A. 18
  • B. 35
  • C. 210
  • D. 343

Correct Answer: C

Explanation:

C

The number of arrangements possible when r are selected from n options is given by . Here, the number of arrangements is = 7 × 6 × 5 = 210.

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 three people, so we need three slots: ___ ___ ___ . For the first slot, 7 people are available as a possible choice, while for the second slot only 6 people are available (as one is taken for the first slot), and for the third slot only 5 people are available (as another was taken away): 7 6 5 . To find the number of arrangements, multiply the numbers in the slots: 210.

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