find the number of ways in which letters of the word 'ARRANGEMENT' can be arranged so that two A's and two R's do not come together.

Question

anonymous · Answer

look..when you have repetitions as A and R and E you divide the permutation by the number off times that letter is repeated....so...

anonymous · Answer

you have 2E's 2A's and 2R's

anonymous · Answer

also 2N's

anonymous · Answer

yes!!

anonymous · Answer

but you want the 2A's and 2R's to come together....so find the total probability and then the probability that the 2A's and 2R's come together then subtract....

anonymous · Answer

*not to come together

anonymous · Answer

thats what i'm not getting what to substract

anonymous · Answer

i rather got 1663200. then i guess i am wrong!

anonymous · Answer

ok...when the 2A's and 2R's come together you consider them as a single letter...say K

anonymous · Answer

so..now you have KNNGMTEE...find this permutation

anonymous · Answer

i've tried that

anonymous · Answer

so what happened?

anonymous · Answer

$$\frac{11!}{2! 2!2!2!}-\frac{8!2!}{2!2!}$$

anonymous · Answer

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