A company has assigned a distinct 3-digit code number to eac

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imane81: Senior | Next Rank: 100 Posts; Posts: 40; Joined: Wed Jan 13, 2010 7:17 pm; Thanked: 1 times; Followed by:1 members

A company has assigned a distinct 3-digit code number to eac

by imane81 » Wed Feb 03, 2010 1:48 pm

Your help on this one is much appreciated. Thanks in advance

A company has assigned a distinct 3-digit code number to each of its 330 employees.
Each code number was formed from the digits
2, 3, 4, 5, 6, 7, 8, 9
and no digit appears more than once in any one code number. How many unassigned
code numbers are there?

A. 6
B. 58
C. 174
D. 182
E. 399

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Source: Beat The GMAT — Problem Solving | Wed Feb 03, 2010 1:48 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

by Ian Stewart » Wed Feb 03, 2010 2:42 pm

imane81 wrote:Your help on this one is much appreciated. Thanks in advance

A company has assigned a distinct 3-digit code number to each of its 330 employees.
Each code number was formed from the digits
2, 3, 4, 5, 6, 7, 8, 9
and no digit appears more than once in any one code number. How many unassigned
code numbers are there?

A. 6
B. 58
C. 174
D. 182
E. 399

To make a code number, we have 8 choices for the first digit, 7 choices for the second digit, and 6 choices for the third digit (subtracting one each time, since we cannot use the same digit more than once), and therefore 8*7*6 = 336 code numbers are possible in total (we just need to multiply the number of choices we have for each digit to find how many code numbers can be made). Since 330 code numbers have been used already, there are 336-330 = 6 unused code numbers.