1985 AHSME Problems/Problem 11
Problem
How many distinguishable rearrangements of the letters in have both the vowels first? (For instance,
is one such arrangement but
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 similarly a total of
possible orderings of the consonants. However, since both T's are indistinguishable, we must divide this total by
. Thus, the actual number of total orderings of consonants is
. Thus 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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