Art of Problem Solving

2005 iTest Problems/Problem 1

Problem

During the $2005$ iTest, you will be introduced to Joe and Kathryn, two high school seniors. If $J$ is the number of distinct permutations of $JOE$, and $K$ is the number of distinct permutations of $KATHRYN$, find $K -J$.

Solution 1

The number of arrangements of the letters in $JOE$ is $3!=6$ and the number of arrangements of the letters in KATHRYN is $7!=5040$. Plugging these in, $K-J=5040-6=\boxed{5034}$

See Also

2005 iTest (Problems, Answer Key)
Preceded by:
First Problem
Followed by:
Problem 2
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