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

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
A certain company places a six-symbol code on each of their products.  [#permalink]

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03 Jan 2019, 04:54
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Difficulty:

15% (low)

Question Stats:

81% (01:07) correct 19% (02:01) wrong based on 48 sessions

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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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Joined: 26 Dec 2018
Posts: 142
Location: India
Re: A certain company places a six-symbol code on each of their products.  [#permalink]

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Updated on: 03 Jan 2019, 06:29
1
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
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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.
Manager
Joined: 26 Dec 2018
Posts: 142
Location: India
Re: A certain company places a six-symbol code on each of their products.  [#permalink]

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03 Jan 2019, 06:24
1
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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Joined: 02 Sep 2009
Posts: 56307
Re: A certain company places a six-symbol code on each of their products.  [#permalink]

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03 Jan 2019, 08:10
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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Concentration: Sustainability, Marketing
GPA: 4
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Re: A certain company places a six-symbol code on each of their products.  [#permalink]

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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] 06 Jan 2019, 05:32
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