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

Find the probability that if the letters of the word "parallel" are randomly arranged that the L's will not be together.

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 8:24am
Treat 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

## Answer this Question

## Related Questions

- Math Help - Permutation and combinations (Trig/alg2 class) In how many ways can ...
- MATH - - Permutation and combinations (Trig/alg2 class) In how many ways can ...
- math - Robert has three boxes of letters: The first box contains the six letters...
- Math - Hi! Can someone check my answers? Thanks!! Directions: Tell whether the ...
- Math - Hi! Can someone check my answers? Thanks!! Directions: Tell whether the ...
- math permutations - how many distinguishable permutations are there of the ...
- 8th grade Algebra - I'm trying to help my young friend -- and am totally lost. ...
- maths-probabilty - find the no. of ways in which letters of the word ARRANGEMENT...
- maths-probabilty - find the no. of ways in which letters of the word ARRANGEMENT...
- Math/ Algebra 2 - How many different ways can the letters in the word ...

More Related Questions