# Forming Combinations with conditions

Suppose B is a finite collection of distinct square matrices of nth order.

And , A a subcollection of B.

I want unique combinations of four distinct elements -three from A and one from B.

I tried this

```
X=Combinations(A,3)
Y=Combinations(B,1)
for i in range(len(X)):
for j in range(3):
for k in range(len(Y)):
if ((X[i])[j])!=(Y[k]):
show(X[i]+Y[k])
```

I know problem is with my "if" command.

My question is how to change the “if” command so that none of the matrices in X[i] equals Y[k], so that we get distinct matrices in a combination.

Further, how to get unique combinations.

Thanks.

Let $C$ be the set difference of $B$ and $A$. Then construct combinations of 3 elements from $A$ and one from $C$, or all 4 elements from $A$.

I think that it is acceptable if all four elements end up coming from

`A`

, so either choose the combination`c`

from`A`

first and then take the set difference of`B`

and`c`

and choose one element from that, or choose one element`y`

from`B`

and take combinations from`B \setminus {y}`

.Yes, it is acceptable if all elements come from A. Thanks for your further insights into the problem.