2005 iTest Problems/Problem 1: Difference between revisions
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==Problem== | |||
During the <math>2005</math> iTest, you will be introduced to Joe and Kathryn, two high school seniors. If <math>J</math> is the number of distinct permutations of <math>JOE</math>, and <math>K</math> is the number of distinct permutations of <math>KATHRYN</math>, find <math>K -J</math>. | |||
==Solution 1== | |||
The number of arrangements of the letters in <math>JOE</math> is <math>3!=6</math> and the number of arrangements of the letters in KATHRYN is <math>7!=5040</math>. Plugging these in, <math>K-J=5040-6=\boxed{5034}</math> | |||
==See Also== | |||
{{iTest box|year=2005|before=First Problem|num-a=2}} | |||
[[Category: Introductory Combinatorics Problems]] | |||
Latest revision as of 18:11, 13 October 2025
Problem
During the 
iTest, you will be introduced to Joe and Kathryn, two high school seniors. If 
is the number of distinct permutations of 
, and 
is the number of distinct permutations of 
, find 
.
Solution 1
The number of arrangements of the letters in is 
and the number of arrangements of the letters in KATHRYN is 
. Plugging these in, 
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: First Problem |
Followed by: Problem 2 | |
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