Problem Solving

Hi,

I thought the answer is E) but correct answer turned out to be C) - Can anyone please explain?? Thanks!

18. If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?
(A) 4 (B) 6 (C) 12
(D) 16 (E) 24

Since the number has to be even, it has to end in either 2 or 6

Possible numbers that can end in 6 = 3! = 6
Possible numbers that can end in 2 = 3! = 6

Hence 12

^^ That is 4C2 + 4C2= 12

For the extension to be an even integer, the unit's digit of the extension has to be even (either 4 or 2 in this case). Hence we have 2 choices for the unit's digit.

Unit's digit = 2 choices (either 4 or 2)
Ten's digit = 3 choices (1 digit has been used)
Hundreads digit = 2 choices (2 have been used)
Thousands digit = 1 remaining choice

= 2*3*2*1 = 12 choices