From the word, FORMULA, five letters are selected at random and arranged in a straight line. What is the probability that if one such arrangement is selected at random that the three vowels are together?

THANKS!!!

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- Mar 14th 2010, 04:24 AMdifferentiatesimple permutations
From the word, FORMULA, five letters are selected at random and arranged in a straight line. What is the probability that if one such arrangement is selected at random that the three vowels are together?

THANKS!!! - Mar 14th 2010, 05:08 AMArchie Meade
There are 7! arrangements of FORMULA

If the 3 vowels are together, take them as a group.

There are 5! arrangements of the group with the other 4 letters.

However the group itself can be arranged in 3! ways.

That's 3!4! arrangements with the vowels together.

If 5 of the 7 are chosen, there are arrangements,

and there are 3! arrangements with the 3 taken as a group,

giving 3!3! arrangements that contain all 3 vowels.

The probability can be calculated then.