Difference between revisions of "1985 AHSME Problems/Problem 11"
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==Problem== | ==Problem== | ||
| − | How many | + | How many distinguishable rearrangements of the letters in <math>CONTEST</math> have both the vowels first? (For instance, <math>OETCNST</math> is one such arrangement but <math>OTETSNC</math> is not.) |
<math> \mathrm{(A)\ } 60 \qquad \mathrm{(B) \ }120 \qquad \mathrm{(C) \ } 240 \qquad \mathrm{(D) \ } 720 \qquad \mathrm{(E) \ }2520 </math> | <math> \mathrm{(A)\ } 60 \qquad \mathrm{(B) \ }120 \qquad \mathrm{(C) \ } 240 \qquad \mathrm{(D) \ } 720 \qquad \mathrm{(E) \ }2520 </math> | ||
Revision as of 00:50, 3 April 2018
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 
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. However, since both T's are indistinguishable, we must divide this total by 
. Thus, the actual number of total orderings of consonants is 
In total, there are 
possible rearrangements, 
.
See Also
| 1985 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
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