If the five letters in the word VOWEL are rearranged, what is the probability the L will preceded the E?

Because there are 5 letters in the word VOWEL we can compute the sample space as previously.

c( S ) =

First, choose two positions for L and E out of the five positions. Positions implies an ordering.

c( G ) =

Let H be the event that the letter L precedes the letter E in the rearrangement.

c( H ) =

Third, let J be the event of placing the letters VOW. Note that the letters VOW can be placed in the remaining three positions in 3! ways

c( J ) =

Fourth, let K be the event that L will precede E in the rearrangement.

Using the multiplication principle in the numerator, and the sample space count in the denominator, we find that the probability that L precedes E is:

P( K ) =