Put a + in each column in such that no row has more than one +. .
That is one way to do this. And that can be one of ways.
Now, change each + to – and each – to plus. How many ways do you have?
Suppose we use 6 +’s and 10 –‘s.
How many ways can we rearrange the columns and rows? Be careful of duplications.
Again change the +’s and –‘s.
Is there another possible scheme?