BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Lottery game

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 682
Joined: Fri Jan 16, 2009 2:40 am
Thanked: 32 times
Followed by:1 members

Lottery game

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
Top
Source: — Problem Solving |
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pm
Thanked: 331 times
Followed by:11 members

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
Top
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pm
Thanked: 331 times
Followed by:11 members

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
Top
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
Top
Legendary Member
Posts: 2467
Joined: Thu Aug 28, 2008 6:14 pm
Thanked: 331 times
Followed by:11 members

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....
Top
User avatar
Legendary Member
Posts: 682
Joined: Fri Jan 16, 2009 2:40 am
Thanked: 32 times
Followed by:1 members

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 !!!
Top
Post new topic Post Reply
• Page 1 of 1