## A company plans to assign identification numbers to its employees. Each number is to consist of four different digits

##### This topic has expert replies
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pm
Followed by:23 members

### A company plans to assign identification numbers to its employees. Each number is to consist of four different digits

by BTGmoderatorDC » Wed Nov 02, 2022 11:55 pm

00:00

A

B

C

D

E

## Global Stats

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

OA B

Source: GMAT Prep

Master | Next Rank: 500 Posts
Posts: 415
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

### Re: A company plans to assign identification numbers to its employees. Each number is to consist of four different digit

by regor60 » Thu Nov 03, 2022 8:06 am
Since 0 can't be the first digit there are

9 choices for the first digit .

For the second digit there are also 9 choices since 0 can be used.

Third digit then

8 choices. And fourth digit

7 choices.

So the total is 9*9*8*7.

Rather than multiplying this out, we can see that the 9*9 will leave a 1 as the first digit, which multiplied by 8 leaves 8 as the first digit, then multiplied by 7 leaves

6 as the first digit.

Only B satisfies

### GMAT/MBA Expert

GMAT Instructor
Posts: 7276
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

### Re: A company plans to assign identification numbers to its employees. Each number is to consist of four different digit

by Scott@TargetTestPrep » Thu Nov 10, 2022 6:00 pm
BTGmoderatorDC wrote:
Wed Nov 02, 2022 11:55 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

OA B

Source: GMAT Prep
There are 9 choices for the first digit (1 through 9, inclusive). The second digit can be any of the 10 digits (0 through 9, inclusive) EXCEPT it can’t repeat the first digit; thus, there are 9 options for the second digit. The third digit can’t repeat either of the first two digits, so there are 8 options. Similarly, the fourth digit can’t repeat any of the first 3 digits, so there are 7 options. Thus, the total number of options is 9 x 9 x 8 x 7 = 4,536.