CA Foundation · Quantitative Aptitude · Permutations and Combinations
In how many ways can 4 different prizes be awarded to 7 employees of a Surat textile firm if no employee can receive more than one prize?
The answer is 840. Because the four prizes are different and no employee can win twice, this is an arrangement of 4 from 7 distinct people, 7P4 = 7×6×5×4 = 840. Choosing without regard to order (35) would undercount.
- A28
- B210
- C840Correct
- D2401
Explanation
Prizes are different, so order matters: 7P4 = 7×6×5×4 = 840. The option 35 would be 7C4, but that ignores which prize each person gets, and 28 is not a valid count here. 2401 = 7^4 allows repeats, which is not permitted.
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