Question

A seamstress is sewing a quilt. She will use 4 different fabrics from the 6 fabrics she has to choose from. She will use 2 different bindings from
the 7 she has to choose from for the edges.
How many different quilts are possible?

the answer is not 315

Answer 1

You're right that 315 = C(6,4)·C(7,2) is one possible count, but that assumes the two bindings are chosen without regard to which edge they go on. The ambiguity is whether the two bindings are placed on distinct edges (so their positions matter) or just chosen as a pair.

Compute the pieces:

- Ways to pick 4 fabrics from 6: C(6,4) = 15.
- Ways to pick 2 different bindings from 7:
- If positions do NOT matter (just an unordered pair): C(7,2) = 21 → total = 15·21 = 315.
- If the bindings are placed on distinct edges (order matters): P(7,2) = 7·6 = 42 → total = 15·42 = 630.

So if the bindings are assigned to specific edges (top vs bottom, inner vs outer, etc.), the answer is 630. If the bindings are only chosen as a pair with no positions, the answer is 315.

Which interpretation does the problem intend?