2004 AMC 8 Problem 17
Attempt Problem 17 of the 2004 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2004 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
Three friends have a total of identical pencils, and each one has at least one pencil. In how many ways can this happen?
Answer: D
Small hint:
Give each friend one pencil first.
Big hint:
Count the ways to distribute the remaining pencils among the friends.
Solution:
First give each friend one pencil. Then pencils remain to distribute among the friends.
If one friend gets all remaining pencils, there are ways. If the remaining pencils split as and there are ways. If each friend gets one more, there is way.
The total number of ways is
Thus, D is the correct answer.
Problem 17 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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