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Each student at a certain university is given a four-charact

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Each student at a certain university is given a four-charact [#permalink] New post 01 May 2013, 08:47
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Each student at a certain university is given a four-character identification code, the …rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?

A. 135,200
B. 67,600
C. 64,000
D. 60,840
E. 58,500
[Reveal] Spoiler: OA

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Re: Each student at a certain university is given a four-charact [#permalink] New post 01 May 2013, 09:01
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manishuol wrote:
Each student at a certain university is given a four-character identification code, the …rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?

A . 135,200
B. 67,600
C. 64,000
D. 60,840
E. 58,500


Four character identification code
_ _ _ _
First two parts for the code, are digits between 0-9, therefore, 10 options for the first part of the code,
and as characters may be repeated, 10 options for the second part as well
Therefore, we have 10 X 10 possibilities for the first and second part of the code

Last two parts of the code, are characters selected from the 26 letters of the alphabet, therefore, 26 options for the third part of the code,
and as characters may be repeated, 26 options for the fourth part as well
Therefore, we have 26 X 26 possibilities for the third and fourth part of the code

so, in all total no. of different identification codes generated following these rules
= 10 X 10 X 26 X 26 = 67600

Answer B

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Each student at a certain university is given a four-char [#permalink] New post 29 Sep 2013, 23:36
Expert's post
Source : Jeff Sackmann Extreme Challenge

Each student at a certain university is given a four-character identification code, the …rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?


(A) 135,200
(B) 67,600
(C) 64,000
(D) 60,840
(E) 58,500

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Re: Each student at a certain university is given a four-char [#permalink] New post 29 Sep 2013, 23:41
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GNPTH wrote:
Source : Jeff Sackmann Extreme Challenge

Each student at a certain university is given a four-character identification code, the …rest two characters of which are digits between 0 and 9, inclusive, and the last two characters of which are selected from the 26 letters of the alphabet. If characters may be repeated and the same characters used in a different order constitute a different code, how many different identification codes can be generated following these rules?


(A) 135,200
(B) 67,600
(C) 64,000
(D) 60,840
(E) 58,500


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Re: Each student at a certain university is given a four-char   [#permalink] 29 Sep 2013, 23:41
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