please help in permutation question

sachin_yadav wrote:Hi All,

Please help in the following question.

A telephone company
My answer is E which is incorrect and i am also aware of this mistake because i calculated this question without using a constraint. i.e Total number of codes = 3 * 3 * 3 = 27(each of the 3 digits can be repeated); however, the constraint says "product of the digits in the area code must be even".

The explanation says, " Number of codes yielding an even product = 27 - 1 = 26. So, answer is D (correct)

My question is :-

Why and what is the logic to subtract 1 from 27 ?

or

In order to get an even value, do we have to subtract 1 from 27 ?

Please advise..

sachin_yadav wrote:Hi All,

Please help in the following question.

A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 5, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created ?


(A) 8

(B) 9

(C) 18

(D) 26

(E) 27


My answer is E which is incorrect and i am also aware of this mistake because i calculated this question without using a constraint. i.e Total number of codes = 3 * 3 * 3 = 27(each of the 3 digits can be repeated); however, the constraint says "product of the digits in the area code must be even".

The explanation says, " Number of codes yielding an even product = 27 - 1 = 26. So, answer is D (correct)

My question is :-

Why and what is the logic to subtract 1 from 27 ?

or

In order to get an even value, do we have to subtract 1 from 27 ?

Please advise..

Now see there is only one possibility of getting odd number when used all 3 digits that is 5*5*5 = 125.

You have to discard this odd number as q asks only about even product.