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A certain identification code is a list of five symbols: S1S

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A certain identification code is a list of five symbols: S1S [#permalink] New post 25 Feb 2017, 08:16
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86% (00:16) correct 13% (01:04) wrong based on 23 sessions


A certain identification code is a list of five symbols: S1,S2,D1,D2,D3. Each of the first 2 symbols must be one of the 26 letters of the English alphabet, and each of the last 3 symbols must be one of the 10 digits. (Repeated letters and digits are allowed.) What is the total number of different identification codes?


A) 1,757,600

B) 676,000

C) 468,000

D) 1,676

E) 82
[Reveal] Spoiler: OA

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Re: A certain identification code is a list of five symbols: S1S [#permalink] New post 04 Mar 2017, 07:40
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Explanation

Now here we have 5 places to fill S1, S2, D1, D2 and D3 respectively. Repetition is allowed

S1: can take vale of 26 alphabets (26 options)
S2: can take vale of 26 alphabets (26 options)
D1: can take vale of 10 digits (10 options)
D2: can take vale of 10 digits (10 options)
D3: can take vale of 10 digits (10 options)

Total no of possibilities = \(S1 \times S2 \times D1 \times D2 \times D3\)= \(26 \times 26 \times 10 \times 10 \times 10\) = 676,000.

Hence B is the correct option.
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Re: A certain identification code is a list of five symbols: S1S [#permalink] New post 07 Sep 2018, 17:57
Hi Sandy, can you explain why we couldn't divide the product of the first two letters by two? Identical letters would count two identical outcomes right? (e.g., AA)
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Re: A certain identification code is a list of five symbols: S1S [#permalink] New post 08 Sep 2018, 12:42
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jasonchung55 wrote:
Hi Sandy, can you explain why we couldn't divide the product of the first two letters by two? Identical letters would count two identical outcomes right? (e.g., AA)


I think you have a valid point! You found a wrong question in the official ETS collection.

Numbers such as: AA123 and AA123 is counted twice!
So there are \(26 \times 1000\) (26 because - AA, BB, CC, ..... ZZ)

We need to substract this number from: 676,000.
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Re: A certain identification code is a list of five symbols: S1S [#permalink] New post 13 Sep 2018, 12:25
Would really like it if the options lit up as Green or Red :D

Ans = 26*26*10*10*10 = 676,000
Re: A certain identification code is a list of five symbols: S1S   [#permalink] 13 Sep 2018, 12:25
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