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Thread: permuatation help

  1. #1
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    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
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  2. #2
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    Re: permuatation help

    Hello, righteous818!

    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.
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