1. In how many ways can the letters of the word POLICEMAN
be arranged if the "word" must begin with L and end with a vowel?
There is 1 way to choose the 1st letter as L.
There are 4 ways to choose the last letter as a vowel.
There are 7! ways to choose the letters in between.
That's 1*4*7! = 20160 ways.
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2. What is the probability that if the letters of POLICEMAN
are randomly placed in a row, the "word" will begin with L and end with a vowel?
20160 ways out of 9! or 
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You can also do the second part without using the first part at all.
The probability of choosing a P first is 1/9.
The probability of then choosing a vowel last in 1/2. [Because when you've
chosen an L first there are 8 letters left, half vowels and half consonants.
So that probability is (1/9)(1/2) = 1/18. (This way you can ignore the
letters in between the first and last.)
Edwin
