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- #1

- Apr 14, 2013

- 4,008

We have the letters 'WINPRESENT'. I want to calculate the rearrangements of these letters that contain either the word 'WIN' or the word 'PRESENT' or both of them.

I have done the following:

The subword 'WIN' is contained in $8!$ rearrangements. Since at 'PRESENT' we have twice the letter E we get $\frac{8!}{2}$ rearrangements. The subword 'PRESENT' is contained in $4!$ rearrangements. We have calculated twice 'WINPRESENT' and twice 'PRESENTWIN'.

So the total amount of rearrangements that contain either the word 'WIN' or the word 'PRESENT' or both of them is equal to $\frac{8!}{2}+4!-2$, or not?

Or do we have to take into account that we have twice the letter N ?