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Question

Difficulty: EasyPermutations

In how many distinct ways can a president, a vice-president, and a secretary be chosen from a group of 77 candidates, assuming no candidate can hold more than one position?

Answer: 210 ways

Answer

The total number of distinct ways to choose the three officers from 7 candidates is 210.
Selecting 3 distinct officers from a group of 7 candidates requires ordering 3 individuals out of 7, which equals 7×6×5=2107 \times 6 \times 5 = 210 ways.

Step-by-Step Solution

1
Identify whether the problem involves permutations or combinations
Order is important because the positions (President, Vice-President, Secretary) are distinct.
Selecting person X as President and person Y as Secretary is different from selecting person Y as President and person X as Secretary.
2
Calculate the permutation 7P3^7P_3
7P3=7×6×5=210^7P_3 = 7 \times 6 \times 5 = 210
There are 7 choices for President, 6 remaining choices for Vice-President, and 5 remaining choices for Secretary.

Key Concept

Permutations of n items taken r at a time
Estimated Time:45s
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Topics

Permutations

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