Lottery game

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Wed Mar 18, 2009 6:46 pm

Entries in a particular lottery game are made up of 3 digits, each 0 through 9. If the order of digits in the entries matters, how many different possible enteries exist in which all 3 digits are not equal?

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

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Source: Beat The GMAT — Problem Solving | Wed Mar 18, 2009 6:46 pm

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Mar 18, 2009 7:05 pm

Hope I dint miss something.

First digit 10 choices including 0 since the problem says 0 can be the first digit

2nd digit->9 choices

3rd digit-> 8 choices

10*9*8 = 720

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Mar 18, 2009 7:20 pm

I did miss something.

2 digits can be equal but not all 3.

10*9*2 =180

But ech of the above picks can be arranged in 3 ways

So 180*3 but we need to divide by 2 since some pairs of arrangement are the same

I pick 1 2 1 and then 2 1 1

3 different numbers can be formed by either of these 2 picks but the resulting unique numbers is just half. Out of 540 only 270 are unique.(hope I dint mess up here, Ian or some one else please correct me)

180*3/2 = 270

So 720+270 = 990

Nice prob.

Regards,
CR

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m&m: Master | Next Rank: 500 Posts; Posts: 134; Joined: Sun Feb 15, 2009 7:44 pm; Thanked: 14 times

by m&m » Wed Mar 18, 2009 7:58 pm

alternatively we could solve this by saying total choices - number of choices with all 3 digits same.

Total choices = 10*10*10
Choices with all 3 digits same = 10 (incld 000, 111, 222, 333)

1000 - 10 = 990

Voila

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Wed Mar 18, 2009 8:21 pm

alternatively we could solve this by saying total choices - number of choices with all 3 digits same.

Total choices = 10*10*10
Choices with all 3 digits same = 10 (incld 000, 111, 222, 333)

1000 - 10 = 990

Well done....

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Vemuri: Legendary Member; Posts: 682; Joined: Fri Jan 16, 2009 2:40 amFollowed by: 1 member; Thanked: 32 times

by Vemuri » Thu Mar 19, 2009 1:14 am

m&m wrote:alternatively we could solve this by saying total choices - number of choices with all 3 digits same.

Total choices = 10*10*10
Choices with all 3 digits same = 10 (incld 000, 111, 222, 333)

1000 - 10 = 990

Voila

Cool approach !!!

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