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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]

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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, 03:20, edited 1 time in total.
Edited the question and added the OA.

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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 employees. Eac [#permalink]

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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]

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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]

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New post 25 Feb 2013, 22:00
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]

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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]

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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]

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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]

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New post 31 Aug 2013, 05:50
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]

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New post 31 Aug 2013, 05:59
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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]

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New post 31 Mar 2014, 08:32
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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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A company plans to assign identification numbers to its empl [#permalink]

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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 26 Nov 2014, 08:53
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 empl [#permalink]

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New post 08 Apr 2016, 10:59
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 of 6.

Answer: B.

Hope it's clear.


I got the same answer almost but I multiplied it by 4! in the end assuming we could rearrange the digits and get a different number. Can you please explain why this is not correct?? Thank you.

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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 09 Apr 2016, 01:47
MeghaP 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 of 6.

Answer: B.

Hope it's clear.


I got the same answer almost but I multiplied it by 4! in the end assuming we could rearrange the digits and get a different number. Can you please explain why this is not correct?? Thank you.


The method used already takes care of all different arrangements. Try to test with smaller numbers to check.
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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 21 Apr 2017, 23:42
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 thing to note is that the possibility of choices is 0-9- which actually is ten numbers if you count [0,1,2,3,4,5,6,7,8,9] yet the first number of the digit cannot have 0 so there is a pool of 9 choices to choose from for the first number

9 x 9 x 8 x 7 =
4536

Thus B

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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 11 May 2017, 21:40
1st digit can be anything from 1 to 9, So 9 possible digits
2nd can be anything from 0 to 9 but not the one used as 1st digit, so again 10- 1 = 9 possible values
3rd can be anything from 0 to 9 except the two digits used as 1st & 2nd digit, so 10-2 = 8 possible values
4th can be anything from 0 to 9 except the 3 digits used as 1st, 2nd and 3rd digit, so 10-3 = 7

Hence total possibilities = 9x9x8x7 = 4536

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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 11 May 2017, 22:48
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


Since we have to form 4 digit number with 1st digit non-zero and all different digits.
It can be formed in following way
1st digit -> 9 ways (1 to 9)
2nd digit -> 9 ways (0 to 9 excluding 1st digit)
3rd digit -> 8 ways ( 0 to 9 excluding 1st and 2nd digit)
4th digit -> 7 ways ( 0 to 9 excluding 1st , 2nd and 3rd digit)
So total no. of ways = 9*9*8*7 = 4536 ways

[Reveal] Spoiler:
So different identification numbers possible : 4536

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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 20 May 2017, 20:25
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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


1. Ordering is important and there is no repetition, so this is an nPr problem
2. Is there a constraint?. The first digit cannot be zero
3. Number of ways the first digit can be selected is 9
4. Number of ways the second third and last digits can be ordered is 9P3
5. Total number of permutations is 9*9*8*7=4536
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Re: A company plans to assign identification numbers to its empl [#permalink]

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New post 26 Jun 2017, 01:28
bethebest 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 of 6.

Answer: B.
-- >
Where in the question has it been mentioned that succeeding digits cannot inherit the preceding value(there is no mentions about repetitions). By that logic, values like 9999 or 9988 or 7777 cannot be used as identification numbers.

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Re: A company plans to assign identification numbers to its empl   [#permalink] 26 Jun 2017, 01:28

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