1985 AHSME Problems/Problem 11
Problem
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.)
Solution
We can separate each rearrangement into two parts: the vowels and the consonants. There are possibilities for the first value and
for the remaining one, for a total of
possible orderings of the vowels. There are
possibilities for the first consonant,
for the second,
for the third,
for the second, and
for the first, for a total of
possible orderings of the consonants. In total, there are
possible rearrangements,
.
See Also
1985 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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