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by yangliu0401 » Wed Feb 18, 2009 4:59 pm
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: Permutation

by x2suresh » Wed Feb 18, 2009 5:03 pm
yangliu0401 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
9*9*8*7=4536

B
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by fleshins » Wed May 20, 2009 8:50 pm
I get 9000

9*10*10*10

Am I missing something?
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by Svedankae » Thu May 21, 2009 4:53 am
fleshins wrote:I get 9000

9*10*10*10

Am I missing something?
the digits have to be distinct. 7777 is not an option for example. thats why it is 9*9*8*7...
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by Davincii » Thu May 21, 2009 5:32 pm
I think 9 x 10 x 10 x 10

For the unit digit: 0-9 = 10
For the tens digit: 0-9 = 10
For the hundreds digit: 0-9 = 10
For the thousands digit; 1-9 = 9

Since the question didn't say nothing if the digits can be repeated, I therefore safely conclude that the digits can be repeated. For example, 1111, 2222

Hope this help
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by fleshins » Thu May 21, 2009 6:24 pm
Davincii wrote:Since the question didn't say nothing if the digits can be repeated
"four different digits"
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by deb1234 » Fri May 22, 2009 11:19 am
I solved it this way:
You can choose 4 digits from 10 digits to make an emplyoee number. Here order is important.
So this will be 10P4.
Now You cannot choose any number starting with 0. How many such numbers can you have? You can choose 3 digits from the remainning 9 numbers for unit, tenth and hundreth position.
That will be 9P3.
The difference is 10P4- 9P3 = 4536 and hence the answer.
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by Scott@TargetTestPrep » Wed Dec 13, 2017 5:02 pm
yangliu0401 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
We have 9 options for the first digit (because the digit 0 can't be used), 9 for the second (since it can't be the same as the first one), 8 for the third (since it can't be the same as either of the first two), and 7 for the fourth (since it can't be the same as any of the first three). Thus, the number of possible identification numbers is 9 x 9 x 8 x 7 = 4,536.

Answer: B

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