Problem Solving

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

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

I get 9000

9*10*10*10

Am I missing something?

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...

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

Davincii wrote:Since the question didn't say nothing if the digits can be repeated

"four different digits"

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.