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A company plans to assign identification numbers to its empl

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A company plans to assign identification numbers to its empl [#permalink] New post 23 Aug 2008, 07:21
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A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000
[Reveal] Spoiler: OA

Last edited by Bunuel on 26 Feb 2013, 02:20, edited 1 time in total.
Edited the question and added the OA.
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Re: PS: couting problem [#permalink] New post 23 Aug 2008, 07:34
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judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

3024
4536
5040
9000
10000


= No. of ways select first digit (other than 0) * No of wasy select second digit (exclude first digit selected) * no of ways select 3rd digit (exclude first 2) * no of ways to select 4 th digit (excllude first 3 digits)
= 9*9*8*6= 4536
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A company plans to assign identification numbers to its employees. Eac [#permalink] New post 09 Mar 2011, 21:08
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A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

A)3,024
B)4,536
C)5,040
D)9,000
E)10,000
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Re: A company plans to assign identification numbers to its employees. Eac [#permalink] New post 09 Mar 2011, 21:20
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A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

A)3,024
B)4,536
C)5,040
D)9,000
E)10,000


First digit (1000th place) can be any of 0 to 9 except 0, so it can be chosen in nine ways

Second digit (100th place) can be any of 0 to 9 except the one already chosen for 1000th place, so it can be chosen in nine ways

Third digit (10th place) can be any of 0 to 9 except the ones already chosen for 1000th place and 100th place, so it can be chosen in eight ways

Fourth digit (units place) can be any of 0 to 9 except the ones already chosen for 1000th place, 100th place and 10th place, so it can be chosen in seven ways

Total number of ways = 9*9*8*7 = 81*56. Only option with 6 in units place is B, so answer is B.
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Re: A company plans to assign identification numbers to its [#permalink] New post 25 Feb 2013, 19:23
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It should be 9*9*8*7 right?
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Re: A company plans to assign identification numbers to its [#permalink] New post 25 Feb 2013, 21:00
Yes. The total number of ways=9*9*8*7

fozzzy wrote:
It should be 9*9*8*7 right?

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Re: A company plans to assign identification numbers to its empl [#permalink] New post 26 Feb 2013, 02:27
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judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000


The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit of 6.

Answer: B.

Hope it's clear.
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Re: A company plans to assign identification numbers to its empl [#permalink] New post 23 Mar 2013, 07:28
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Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000


The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.


Hi Bunnel,

I took 9*10*10*10=9000 i thought he didn't mention any thing such as repetition not allowed or not allowed may i know if i misread the question?

May i know where i went wrong?
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Re: A company plans to assign identification numbers to its empl [#permalink] New post 23 Mar 2013, 07:52
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mydreammba wrote:
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000


The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.


Hi Bunnel,

I took 9*10*10*10=9000 i thought he didn't mention any thing such as repetition not allowed or not allowed may i know if i misread the question?

May i know where i went wrong?


"Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0"
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Re: A company plans to assign identification numbers to its empl [#permalink] New post 31 Aug 2013, 04:50
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000


The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.



why can't it be 9 * 10 * 10* 10 ?
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Re: A company plans to assign identification numbers to its empl [#permalink] New post 31 Aug 2013, 04:59
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SUNGMAT710 wrote:
Bunuel wrote:
judokan wrote:
A company plans to assign identification numbers to its employees. Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0. How many different identification numbers are possible?

(A) 3,024
(B) 4,536
(C) 5,040
(D) 9,000
(E) 10,000


The first digit can take 9 values from 1 to 9 inclusive;
The second digit can also take 9 values (9 digits minus the one we used for the first digit plus 0);
The third digit can take 8 values;
The fourth digit can take 7 values.

Total = 9*9*8*7 = something with the units digit if 6.

Answer: B.

Hope it's clear.



why can't it be 9 * 10 * 10* 10 ?


Check the post just above yours: "Each number is to consist of four different digits from 0 to 9, inclusive, except that the first digit cannot be 0"
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Re: A company plans to assign identification numbers to its empl [#permalink] New post 31 Mar 2014, 07:32
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Four DIFFERENT digits. 9*9*8*7.

Only answer with units digit 6 is B.

Hope this helps
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GMAT Prep - Questions where I got stuck [#permalink] New post 28 Oct 2014, 05:47
Hi every one,

I just finished my first GMAT mock, and the experience was not very good. I am attaching a problem - please help me with its solution.

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A company plans to assign identification numbers to its empl [#permalink] New post 28 Oct 2014, 06:36
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omegacube wrote:
Hi every one,

I just finished my first GMAT mock, and the experience was not very good. I am attaching a problem - please help me with its solution.

Omegacube


Merging similar topics. Please refer to the discussion above and ask if anything remains unclear.

Check Constructing Numbers, Codes and Passwords in our Special Questions Directory.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1, and 3. Thank you.


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Re: A company plans to assign identification numbers to its empl [#permalink] New post 28 Oct 2014, 07:29
Thanks...I had missed the 'different' bit...
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Re: A company plans to assign identification numbers to its empl [#permalink] New post 26 Nov 2014, 07:53
When you start from the right hand side (from the 4th digit) you should get the same result but "magically" it doesn't. Can someone explain?
What I mean is this: lets say the number is xyzt. t can take 10 digits, z can take 9 digits, y can take 8 digits and x can take 7-1=6 digits (deducting 1 for the "0" that it cannot take). The total number for probabilities is 10*9*8*6, which is different from 9*9*8*7. Can someone explain why we cannot do this version?
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Re: A company plans to assign identification numbers to its employees. Eac [#permalink] New post 10 Dec 2014, 19:52
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Re: A company plans to assign identification numbers to its employees. Eac   [#permalink] 10 Dec 2014, 19:52
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