H2 maths p&c

Three letter are selected at random from the word pioneer . Find the probability that e selection does not contain the letter E.

Ans is 2/7

What i did:

Total number of ways to choose 3 letters without an restriction

Case 1: both Es selected 5C1

Case 2: all 3 letters unique 6C3

Number of ways to choose 3 letters without E 5c3

Probability 5c3 / (5c1+ 6c3 )

Is there something wrog with my reasoning ?

Hi,

You missed out a third possibility - no Es, whose number of ways = 5C3.

Number of ways without restriction could directly be calculated, as 7C3.

Thanks.

Cheers,
Wen Shih