Math

posted by .

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?

• Math -

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

Similar Questions

1. Finite Math

Please help with this problem. In a student writing contest with 25 entries, 3 essays are selected for first, second, and third place awards and 5 are selected for honorable mention. How many ways can this be done?
2. alg2/trig

I got this question wrong on my test, and I have to correct it :/ How many permutations are there of all the letters in the word "TEXAS" ?
3. probability & statistics

How many distinguishable permutations of letters are possible in the word COLORADO?
4. math permutations

how many distinguishable permutations are there of the letters in the word effective
5. math

Determine the number of permutations of the letters of the word "EFFECTIVE"
6. Permutations

What is the number of permutations for the words: QUEUE COMMITTEE PROPOSITION BASEBALL You can arrange it in any order. You can also arrange it into any order of the letters. You could use the math from FACTORIAL. I need an answer …
7. Math

Hi! Can someone check my answers? Thanks!! Directions: Tell whether the following questions are either permutations or combinations. 1.) Number of ways the Junior class can elect a committee of officers - President, Vice President,
8. Math

Hi! Can someone check my answers? Thanks!! Directions: Tell whether the following questions are either permutations or combinations. 1.) Number of ways the Junior class can elect a committee of officers - President, Vice President,
9. statistics

15. The probability that a recently offered stock by a technology company will double in value within the next three months is 90%. The conclusion regarding this probability estimate was reached based on the opinion of the experts …
10. Pre-Algebra Permutations and Combinations

16. Simplify 6p2 30 15 12 720 17. Simplify 8c5 6,720 336 56 10 Okay, so the formula for Permutations is n!/(n-r)! and the formula for Combinations is n!/r!(n-r)! however I don't quite know how to figure either of these out. I'm sort …

More Similar Questions