# permuatation help

• Mar 19th 2013, 06:59 PM
righteous818
permuatation help
hwo many arrangements of ISOSCELES can be done if no 2 letters of clsss can be together , i have tried many times but never could get the answer the answer is 240 please help me
• Mar 19th 2013, 08:44 PM
Soroban
Re: permuatation help
Hello, righteous818!

Quote:

How many arrangements of ISOSCELES can be done if no 2 letters of CLSSS can be together?

We have 9 spaces to fill.

. . $\_\_\;\square\;\_\_\;\square\;\_\_\;\square\;\_\_ \;\square\;\_\_$

Place $\{E,E,I,O\}$ in the four boxes.
. . There are: $\frac{4!}{2!} = 12$ ways.

Place $\{C,L,S,S,S\}$ in the five blanks.
. . There are: $\frac{5!}{3!} = 20$ ways.

Therefore, there are:. $12\cdot20 \,=\,240$ arrangements.