Take the 2-minute tour ×

We a homework question that asks us to find the 3 letter arrangement of the word "Silly". Here is the exact question.

How many three-letter arrangements are there of the letters taken from the word SILLY?

What I did was do $5P3/2!$ and I ended up getting 30. The answer is 33. What am I doing wrong?


I have just realized, should I be adding back 3 because of a permutation that does have the LL's in it?

share|improve this question
When you choose three letters out of 5, one of the possibilities is S,I,L which has no repetitions. So dividing by $2!$ is wrong. –  Isomorphism Dec 14 '12 at 10:36
What should be the correct step then? –  Jeel Shah Dec 14 '12 at 10:37

1 Answer 1

up vote 2 down vote accepted

In this small problem the easy way is to note first that there are $4\cdot3\cdot2=24$ ways to pick three different letters and permute them. Then observe that there are $3$ ways to pair LL with one of the other letters, and $3$ ways to place that odd letter relative to the two L’s, so there are $3\cdot3=9$ more $3$-letter arrangements that include both L’s, for a total of $24+9=33$ arrangements.

share|improve this answer

Your Answer


