2020 AMC 8 Problem 23
Attempt Problem 23 of the 2020 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2020 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
23.
Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?
Answer: B
Small hint:
Start with unrestricted distributions
Big hint:
Use inclusion-exclusion for students receiving no awards
Video solution:
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Written solution:
There are ways to give each of the distinct awards to one of the students.
Subtract the distributions in which at least one student receives no award. If a particular student receives none, the awards go to the other two students in ways. This gives counts, but the cases in which one student receives all awards have each been subtracted twice.
By inclusion-exclusion, the desired number is
Thus, the correct answer is B.
Problem 23 in other years
- 1985 AMC 8
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- 1987 AMC 8
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- 1989 AMC 8
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