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A certain company places a six-symbol code on each of their products.

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Bunuel
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A certain company places a six-symbol code on each of their products. [#permalink] New post   03 Jan 2019, 04:54
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A certain company places a six-symbol code on each of their products. The first two symbols are one of the letters A–E and the last four symbols are digits. If repeats are allowed on both letters and numbers, how many such codes are possible?

(A) 250000
(B) 350000
(C) 450000
(D) 550000
(E) 600000
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A
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UB001
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Re: A certain company places a six-symbol code on each of their products. [#permalink] New post   Updated on: 03 Jan 2019, 06:29
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Given :
A six-symbol code of which the first two symbols are one of the letters A–E
and the last four symbols are digits.
repeats are allowed both letters and numbers,


Question: how many such odes are possible?


AANNNN
Let us denote the code by AANNNN, where A for Alphabets from A to E, and N for numbers from 0 to 9.
Alphabets are 5 (A, B, C, D, E) & Numbers are 10 (0 to 9)

Since repeats are allowed alphabets can take 5 positions each for the first two letters, and numbers can take 10 positions each for the 4 positions each for the next four remaining letters of the code.

Therefore,
A A N N N N
5 x 5 x 10 x 10 x 10 x 10 = 250,000
Answer Option A is correct.

Originally posted by UB001 on 03 Jan 2019, 06:22.
Last edited by UB001 on 03 Jan 2019, 06:29, edited 1 time in total.
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Re: A certain company places a six-symbol code on each of their products. [#permalink] New post   03 Jan 2019, 06:24
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Bunuel wrote:
A certain company places a six-symbol code on each of their products. The first two symbols are one of the letters A–E and the last four symbols are digits. If repeats are allowed on both letters and numbers, how many such odes are possible?

(A) 250000
(B) 350000
(C) 450000
(D) 550000
(E) 600000


Hi Bunuel,
There's a typo in the last sentence. Please correct odes to codes.
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Bunuel
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Re: A certain company places a six-symbol code on each of their products. [#permalink] New post   03 Jan 2019, 08:10
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UB001 wrote:
Bunuel wrote:
A certain company places a six-symbol code on each of their products. The first two symbols are one of the letters A–E and the last four symbols are digits. If repeats are allowed on both letters and numbers, how many such odes are possible?

(A) 250000
(B) 350000
(C) 450000
(D) 550000
(E) 600000


Hi Bunuel,
There's a typo in the last sentence. Please correct odes to codes.

_______________
Edited. Thank you.
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Re: A certain company places a six-symbol code on each of their products. [#permalink] New post   06 Jan 2019, 05:32
Bunuel wrote:
A certain company places a six-symbol code on each of their products. The first two symbols are one of the letters A–E and the last four symbols are digits. If repeats are allowed on both letters and numbers, how many such codes are possible?

(A) 250000
(B) 350000
(C) 450000
(D) 550000
(E) 600000



first two = 5*5
last 4 = 10*10*10*10

total 25*10^4 IMO A
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Re: A certain company places a six-symbol code on each of their products. [#permalink] New post   02 Jul 2020, 06:38
I wish the argument would have specified it was letters A,B,C,D,E...as it appears only as A, E, a bit confusing.
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Re: A certain company places a six-symbol code on each of their products. [#permalink] New post   24 Aug 2020, 00:35
Bunuel wrote:
UB001 wrote:
Bunuel wrote:
A certain company places a six-symbol code on each of their products. The first two symbols are one of the letters A–E and the last four symbols are digits. If repeats are allowed on both letters and numbers, how many such odes are possible?

(A) 250000
(B) 350000
(C) 450000
(D) 550000
(E) 600000


Hi Bunuel,
There's a typo in the last sentence. Please correct odes to codes.

_______________
Edited. Thank you.

Hi Bunuel,

Can you help explained why we cant use P(5,2)* P(10,4) for this question? Because this formula will exclude the repetitions such as AA, EE, 4444 ? Thank you!
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Re: A certain company places a six-symbol code on each of their products. [#permalink]
24 Aug 2020, 00:35
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