# Thread: Number of Solutions help

1. ## Number of Solutions help

Hey I need some help with this problem:

How many solutions in natural numbers are there to the equation a + b + c + d = 12 where a and b are odd?

I am hoping someone can show me the steps on how to go about doing this so I will understand how to do this problem thanks.

2. ## Re: Number of Solutions help

substitute a=2A+1,b=2B+1,c=2C+1 d=2D+1 and consider the number of non negative integer solutions of A+B+C+D=4.

3. ## Re: Number of Solutions help

Ok so I substituted and ended up with
A+B+C+D = 4 so the possible solutions for a b c d is 1?

4. ## Re: Number of Solutions help

Now the number of solutions is the bonomial coefficient C(4+4-1,4-1)=C(7,3)=35

5. ## Re: Number of Solutions help

Originally Posted by hedi
substitute a=2A+1,b=2B+1,c=2C+1 d=2D+1 and consider the number of non negative integer solutions of A+B+C+D=4.
You should note that the OP requires only a & b be odd.
Look at the coefficient of $x^{12}$ in this expansion.

Thanks Plato