Difference between revisions of "1985 AHSME Problems/Problem 11"
Freddylukai (talk | contribs) (→Solution: changed answer) |
|||
| Line 9: | Line 9: | ||
==See Also== | ==See Also== | ||
{{AHSME box|year=1985|num-b=10|num-a=12}} | {{AHSME box|year=1985|num-b=10|num-a=12}} | ||
| + | {{MAA Notice}} | ||
Revision as of 13:00, 5 July 2013
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. 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
