is there anything harder than teaching permutations and combinations? Of all the subjects and standards I get into, this is the toughest (for me.) After I go through the discussion about "does order matter" and work through some examples to help kids reason through the wording, I feel like I have "fired all my bullets" on this topic. Any hints? strategies? thoughts? If not, I'd settle for a good joke or story to make me laugh. regards.

I, myself, always got screwed up by the phrase, order matters. I have to think of it as, has to be in same order for permutation. Then I see that other orders are different items. The most clear explanation I've found is on www.mathisfun.com . But, just knowing, even, that order matters doesn't tell kids what it means. You have to follow it with... So, you can have groups with the same things in a different order. You probably know this already, but I am so with you on this point.

Probability has been one of the boring subjects, I think and it is kind of separate and transcendental. It starts out with simple ideas, but I think it gets complicated fast - to fast. Permutations are understood by tree diagrams. For combinations you can divide out the number of ways that order doesn't matter, or something like that. I question whether subjects should escalate in difficulty faster than most get motivated: don't move ahead faster than you can think or be motivated.

How about sports. A professional baseball roster has 25 players; 9 play at a time. For simplicity let's assume the order does not matter on defense but it does matter with the line-up on offense. Combination vs permutation. Who would have thought statistics could make baseball interesting!

What is the question? Is the answer.... 25!/(25-9)! for line-up? Is the answer 25!/[(9!)(25-9)! for defense?

Tree diagrams for combinations, in my book - though there's much to be said for demonstrating relatively simple cases of both with offbeat manipulatives like Lego figures, and having students actually count the outcomes.

Yes. Question: A baseball roster has 25 players. How many ways can you line 9 of them up for batting (order matters)? How many ways can you place them on defense assuming they do not play specific positions (ie any of the 25 could play pitcher, catcher, short stop, etc... and order does not matter)? as you said 25!/(25-9)! for the ordered set 25!/9!(25-9)! for the unordered set have someone else check that just to be sure... i'm pretty new to teaching...