# Thread: 3's and 5's that equal 16

1. ## 3's and 5's that equal 16

Hi, I'm new here and very poor at math in general. I'm wondering, is there a simple formula of sorts for finding out how many combinations of two different numbers there are that equal another number? For example, how many combinations of 3's and 5's are there that equal 16? Such as, 3-5-3-5, 3-3-5-5, 3-5-5-3, 5-5-3-3 and 5-3-3-5. Thanks

Mike

2. For your example, two 3's and two 5's add up to 16. That is, total 4 numbers are here among which 2 are same and the rest 2 are also same.

Note that, if there are $\displaystyle N$ elements among which $\displaystyle N_1$ are of one type, $\displaystyle N_2$ are of another type,........,lastly $\displaystyle N_k$ are of another type, where $\displaystyle N_1+N_2+.......+N_k=N$, then the total number of possible combinations is $\displaystyle \frac{N!}{N_1! N_2! .... N_k!}$. Compare this to you problem. What do you get then?

4. Further hint:- You have only $\displaystyle N_1$ and $\displaystyle N_2$, each equals $\displaystyle 2$, and $\displaystyle N=N_1+N_2=4$. Now think.