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#1 2012-01-08 05:22:16
- juantheron
- Member
- Registered: 2011-10-19
- Posts: 312
lucky no. probability
a 4 digit number(numbered from 0000 to 9999) is said to be lucky if sum of its first two digits is same as the sum of its last 2 digits.If a four-digit number is picked up at random,the probability that it is a lucky number is
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#2 2012-01-08 05:51:24
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: lucky no. probability
Hi;
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2012-01-08 15:36:52
- juantheron
- Member
- Registered: 2011-10-19
- Posts: 312
Re: lucky no. probability
Thanks bobbym how can you get it
plz explain me
is it a olympiad question
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#4 2012-01-08 15:50:33
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: lucky no. probability
Hi;
is it a olympiad question
Is it tough to do without generating functions and some complex analysis. Yes, it appears in some books for advanced combinatorics.
The problem can be turned into a bijection with the number of solutions of this diophantine equation.
With 0 ≤ a,b,c,d ≤ 9
The solution method first shows up in a problem I posted here years ago called the 2 beats 3 problem. Of course other people are now claiming they did it first. Anyway A is best solved using a generating function;
We can now just expand the 4 polynomials to get:
See the constant term 670, that is the answer. There are other ways to get the constant term but they require more mathematics.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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