Counting points

My cribbage buddies and I are having an argument about how to count your hand.
Example: I have 6,6,K,7 and a 3 on the cut. I count 4 points, 2 for the pair and 2 for the 15. His math says 8 points because he can count the 3,6,6 three different ways: 6+6+3, 3+6+6, and 6+3+6. I disagree because he's using the EXACT same cards to reach 15. Could I get some clarification on this issue please.

Re: Counting points

You are quite right. You can only count any given cards once. It doesn't matter if you arrange them in a different order, they are still the same cards, and they can only be used once in each combination to make 15.

By contrast, if you had, say, 6-6-3-3, then you could make 15 two ways: once with each of the 3s. You can use the 6s again this time, so long as you combine them with a different 3.