A random three-letter string is to be formed from the letters A, B, C, D, E and F without repetition. a. What is the probability that the string will begin wi

Question

A random three-letter string is to be formed from the letters A, B, C, D, E and F without repetition.

a.
What is the probability that the string will begin with a vowel?

b.
What is the probability that the string will end with a consonant?

c.
What is the probability that the string will consist of all vowels?

d.
What is the probability that the string will consist of all consonants?

e.
What is the probability that the string will consist of a combination of vowels and consonants?

Answer 1

a. 2 out of the 6 letters are vowels, so the probability that the first letter chosen will be a vowel is 1/3.

b. same idea as a.

c. since you have three letters without repetition, and only two vowels, the probability is 0.

d. There are 6!/3! (or 6P3) possible strings. Out of those only 4P3 consist of only consonants. So the probability should be 4P3/6P3

e. See d. Subtract your answer from 1, and you get the remaining probability.