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

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- Mar 19th 2013, 06:59 PMrighteous818permuatation 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 PMSorobanRe: 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.

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

Place $\displaystyle \{E,E,I,O\}$ in the four boxes.

. . There are: $\displaystyle \frac{4!}{2!} = 12$ ways.

Place $\displaystyle \{C,L,S,S,S\}$ in the five blanks.

. . There are: $\displaystyle \frac{5!}{3!} = 20$ ways.

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