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?

 Mar 27, 2020

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 Mar 27, 2020

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:  6C3  =  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:  2C1  =  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:  4C2  =  6.


So, the probability of choosing an E or an O but not both is:  4C2 ·2C1 / 6C3  =  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:  2C2  =  1.

You must now choose one letter from the set of four remaining letters; 4C1  =  4. 


So, the probability fo choosing both an E and an O is:  4C1 · 2C2 / 6C3   =  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.

 Mar 28, 2020

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