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August 1, 2014

Posted by **Candice** on Thursday, October 11, 2012 at 5:47am.

In class, I'm studying permutations and combinations. The solutions stated the no. of permutations where 3 L's are together is 6!/2!. Could you please explain why?

Thanks in advance

- Math -
**Reiny**, Thursday, October 11, 2012 at 8:24amTreat the LLL as if they were one element, say X

so we have

X a a p r e, 6 elements of which two are alike, the two a's

number of ways to arrange them is 6!/2!

(remember we divide by 2! because of the two "alikes" )

So in the first part, the number of ways to arrange the original is

8!/(3!2!) = 3360

The number of ways the LLL is together is 6!/2! = 360

Number of ways the L's are NOT together = 3360 - 360 = 3000

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