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Probability

by amsm25 » Sun May 13, 2012 4:24 am
What percent of the different arrangements of the letters of the word ABACUS are those in which the vowels appear together?

1)10
2)20
3)40
4)60
5)50

OA- 2)20
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by sam2304 » Sun May 13, 2012 5:15 am
ABACUS is a 6 letter word

We are to find ways in which all the vowels stay together.

Consider all the vowels to be a single word. Now we have 4 words with 3 consonants and 1 group word. So arranging them is 4!. The three vowels in the group can be arranged in 3! ways. We have two A as so there is no difference whenever they are together. Divide by 2!

4! * 3!/2!. = 72

Total ways = 6!/2! = 360 [same as above two A's and irrespective of their position when they are together, the count does not increase]

72 is 20% of 360. Hence B.
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