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If all of the telephone extensions in a certain.........

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by Vincen » Wed Jan 24, 2018 8:25 am
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

The OA is the option C.

How can I solve this PS question? I should use combinations or permutations? Experts, I will wait for your answer. Thanks in advanced.
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If all of the telephone extensions in a certain.........

by regor60 » Wed Jan 24, 2018 9:49 am
Check the wording of the question.

The question wording allows for a digit to be used more than once [no it doesn't, what was I thinking !] , but the answer suggests that this is not the intended interpretation
Last edited by regor60 on Fri Jan 26, 2018 6:23 am, edited 1 time in total.
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by [email protected] » Wed Jan 24, 2018 7:13 pm
Hi Vincen,

We're told that all of the telephone extensions in a certain company must be EVEN numbers, and each of the extensions uses each of the four of the digits 1, 2, 3, and 6. We're asked for the number of four-digit extensions that the company can have under these conditions. This question can be solved with a Permutation or by simply listing out all of the possibilities:

Since we're asked for all of the 4-digit numbers, each of the digits (1, 2, 3 and 6) must be used exactly ONCE. Since the 4-digit number must be EVEN, the 4th digit must be either 2 or 6. Starting with that 'restriction', there are 2 options for the 4th digit. Once we place one of those numbers....
There will then be 3 remaining options for the 1st digit. Once we place one...
There will then be 2 remaining options for the 2nd digit. Once we place one...
There will then be 1 remaining option for the 3rd digit.

Total options = (2)(3)(2)(1) = 12 possible 4-digit numbers.

Final Answer: C

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by Jeff@TargetTestPrep » Mon Jan 29, 2018 9:46 am
Vincen wrote: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
If we let 6 be the last digit, then we have 3! = 6 options for the other 3 digits. If we let 2 be the last digit, we have 6 options also. Therefore, we have a total of 12 options.

Answer: C

Jeffrey Miller
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[email protected]

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