Answer:
20160 ways
Probability = 0.0556
Step-by-step explanation:
We have 9 different letters, so the total number of words we can make is:
[tex]Total = 9! = 362880\ words[/tex]
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:
[tex]N = 4 * 7! = 4*7*6*5*4*3*2 = 20160\ words[/tex]
The probability is calculated by the division of the number of words we want over the total number of words:
[tex]P = N / Total = 20160 / 362880 = 0.0556[/tex]
