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
500 ps tet22 #18
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- jayhawk2001
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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
Possible numbers that can end in 6 = 3! = 6
Possible numbers that can end in 2 = 3! = 6
Hence 12
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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
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