1985 AMC 12 Problem 11
Attempt Problem 11 of the 1985 AMC 12 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 1985 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
11.
How many distinguishable rearrangements of the letters in CONTEST have both the vowels first? (For instance, OETCNST is one such arrangement, but OTETSNC is not.)
Answer: B
Small hint:
Order the two vowels in the first two positions
Big hint:
Permute the remaining five letters while accounting for the repeated
Solution:
The vowels can be ordered first in ways. The remaining letters can be arranged in distinguishable ways because the two ’s agree. The total is
Thus the correct answer is B.
Problem 11 in other years
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