All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
tic-tac-toe (Posted on 2004-07-30) Difficulty: 3 of 5
If I put nine pieces of paper, with a digit from 1-9 written on each one, into a hat, and pull 3 out without replacement, what is the likelihood that I will select three numbers that result in a winning tic-tac-toe?
 1 | 2 | 3 
---+---+---
 4 | 5 | 6 
---+---+---
 7 | 8 | 9 

See The Solution Submitted by ThoughtProvoker    
Rating: 1.8333 (6 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Puzzle Solution Comment 14 of 14 |
(In reply to Answer by K Sengupta)

Since 3 numbers are drawn without replacement from the 9 available numbers, the total number of ways this is possible is comb(9, 3) = perm(9, 3)/3! = 504/6 = 84

Now, one can choose three numbers, disregarding order, in the following manner to produce a winning combination,:

** Along the row: (1,2,3), (4,5,6), (7,8,9), so the number of ways is 3
** Along the columns: (1,4,7), (2,5,8), (3,6,9), so the number of ways is 3
** Along the main diagonals: (1,5,9), (3,5,7), so the number of ways is 2

Thus, we have a total of 3+3+2 = 8 distinct winning combinations.

Consequently, the required probabiblity is 8/84 = 0.095238(approx.) 


  Posted by K Sengupta on 2008-03-06 10:50:22
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (7)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information