CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
In how many ways can 5 different prizes be distributed among 3 students if any student may receive any number of prizes, including none?
There are 243 ways. Each of the 5 different prizes independently has 3 possible recipients, so by the multiplication principle the total is 3 raised to the power 5, which equals 243. Using 5 cubed gives 125, which reverses the roles.
- A15
- B60
- C125
- D243Correct
Explanation
Each prize can go to any of 3 students independently, so the total is 3 × 3 × 3 × 3 × 3 = 3^5 = 243. The value 125 = 5^3 reverses the base and exponent, as if students were choosing prizes.
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