
Algebra PreAlgebra and Basic Algebra Math Forum 
 LinkBack  Thread Tools  Display Modes 
March 26th, 2008, 12:25 AM  #1  
Newbie Joined: Mar 2008 Posts: 1 Thanks: 0  Problem related to Cricket (Permutation & Combination)
Hi All, Please help me out with this problem..it's eating me for a long time now Quote:
Satya  
June 18th, 2009, 08:09 PM  #2 
Newbie Joined: Jun 2009 Posts: 9 Thanks: 0  Re: Problem related to Cricket (Permutation & Combination)
We have equation: X1 + X2 + X3 + X4 + X5 + X6 = 14 with condition 0 ? X1, X2, X3, X4, X5, X6 ? 4 and Xi integer (i = 1 > 6) The total roots of above equation is the ways a batsman can score 14 runs The above equation have 1506 roots as below: 0 0 2 4 4 4 0 0 3 3 4 4 0 0 3 4 3 4 0 0 3 4 4 3 0 0 4 2 4 4 0 0 4 3 3 4 0 0 4 3 4 3 0 0 4 4 2 4 0 0 4 4 3 3 0 0 4 4 4 2 0 1 1 4 4 4 0 1 2 3 4 4 0 1 2 4 3 4 ....... 4 4 2 4 0 0 4 4 3 0 0 3 4 4 3 0 1 2 4 4 3 0 2 1 4 4 3 0 3 0 4 4 3 1 0 2 4 4 3 1 1 1 4 4 3 1 2 0 4 4 3 2 0 1 4 4 3 2 1 0 4 4 3 3 0 0 4 4 4 0 0 2 4 4 4 0 1 1 4 4 4 0 2 0 4 4 4 1 0 1 4 4 4 1 1 0 4 4 4 2 0 0 (I can't post a full list of roots because very long. If you want I will send by attachment file) Conclusion have 1506 ways a batsman can score 14 runs in 6 balls not scoring more than 4 runs in any ball. 
December 2nd, 2009, 01:41 PM  #3 
Senior Member Joined: Dec 2009 From: Las Vegas Posts: 209 Thanks: 0  Re: Problem related to Cricket (Permutation & Combination)
Hi satyabrata_pati; The easiest way to solve that problem is to use an ordinary generating function. For the conditions a+b+c+d+e+f = 14 where 0 <= a,b,c,d,e,f <=4 you have the generating function. And you are interested in the coefficient of x^14, that will be tha answer. Expanding that expression we get: The coefficient for x^14 is 1506 so there are 1506 ways. The nice thing about gf's is that they solve the problem entirely. To see how many ways to get 20 runs just check the coeff. of x^20. 
December 6th, 2009, 04:53 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,746 Thanks: 2133 
Moved from Math Olympiads forum.


Tags 
combination, cricket, permutation, problem, related 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Permutation and Combination Problem.  hanzel.michael  Algebra  2  April 4th, 2012 06:15 AM 
Problem on Permutation Combination  raminder  Algebra  3  July 5th, 2011 10:44 AM 
Please help! Permutation and Combination problem  callmethomas  Advanced Statistics  0  January 12th, 2010 05:53 PM 
Combination permutation problem HELP!  erogol  Algebra  2  March 5th, 2009 06:03 AM 
Permutation or combination??  binshehab  Abstract Algebra  2  June 5th, 2008 02:29 PM 