Entries in a particular lottery game are made up of three digits, each 0 through 9. If the order of digits in the entrie

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by M7MBA » Thu Jul 30, 2020 11:29 am

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Entries in a particular lottery game are made up of three digits, each 0 through 9. If the order of digits in the entries matters, how many different possible entries exist in which all three digits are not equal?

A. 516
B. 720
C. 989
D. 990
E. 1321

[spoiler]OA=D[/spoiler]

Source: Princeton Review

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Source: Beat The GMAT — Problem Solving | Thu Jul 30, 2020 11:29 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8155; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: Entries in a particular lottery game are made up of three digits, each 0 through 9. If the order of digits in the en

by Scott@TargetTestPrep » Sun Aug 02, 2020 8:54 am

M7MBA wrote: ↑
Thu Jul 30, 2020 11:29 am
Entries in a particular lottery game are made up of three digits, each 0 through 9. If the order of digits in the entries matters, how many different possible entries exist in which all three digits are not equal?

A. 516
B. 720
C. 989
D. 990
E. 1321

[spoiler]OA=D[/spoiler]

Solution:

There are a total of 10 x 10 x 10 = 1000 entries of the lottery game, and only 10 of them have all three digits that are equal: 000, 111, 222, …, 999. Therefore, 1000 - 10 = 990 entries exist in which all three digits are not equal.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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