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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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Re: A company plans to assign identification numbers to its [#permalink] New post 25 Feb 2013, 19:23
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
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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Expert's post
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
Expert's post
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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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A company plans to assign identification numbers to its empl [#permalink] New post 31 Mar 2014, 07:32
Four DIFFERENT digits. 9*9*8*7.

Only answer with units digit 6 is B.

Hope this helps
Cheers
J
Re: A company plans to assign identification numbers to its empl   [#permalink] 31 Mar 2014, 07:32
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