Three letters are chosen at random from the word POSTER. What is the probability that the selection will contain E or O but not both? E or O or both?

Guest Mar 27, 2020

#2**0 **

There are a total of 6 distinct letters in the word POSTER.

The number of ways to choose three letters from these six letters is: _{6}C_{3} = 20.

To choose a set that contains an E or an O but not both, you must choose one of these two letters and the

number of ways to choose one letter from a set of two is: _{2}C_{1} = 2.

The other two letters must come from this set of four letters: {P, S, T, R}. The number of ways to choose two

letters from a set of four is: _{4}C_{2} = 6.

So, the probability of choosing an E or an O but not both is: _{4}C_{2} ·_{2}C_{1} / _{6}C_{3} = 6·2 / 20 = 12/20.

If you are to choose both the E and the O, you must choose two letters from a set of two: _{2}C_{2} = 1.

You must now choose one letter from the set of four remaining letters; _{4}C_{1} = 4.

So, the probability fo choosing both an E and an O is: _{4}C_{1} · _{2}C_{2} / _{6}C_{3} = 4 · 1 / 20 = 4/20.

To select either one of the two vowels or both of the vowels, add these two answers together:

12/20 + 4/20 = 16/20.

geno3141 Mar 28, 2020