Question

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? & What is the probability the 'word will begin with L and end with a vowel?

Answer 1

20160 ways

Probability = 0.0556

Explanation:

We have 9 different letters, so the total number of words we can make is:

`Total = 9! = 362880\ words`

If we want just the words that begin with L and end with a vowel, we would have the first letter "locked", so we have 8 letters remaining, and it must end with a vowel, so the last "slot" has just 4 possible values (A, E, I or O). Then we would have 4 possible values for the last letter and 7 remaining letters in the middle of the word:

`N = 4 * 7! = 4*7*6*5*4*3*2 = 20160\ words`

The probability is calculated by the division of the number of words we want over the total number of words:

`P = N / Total = 20160 / 362880 = 0.0556`