Cracking Combinations & Permutations (Counting & Listing)

Here is just a quick overview of how I approach combination or permutation questions. You know, the ones that say if there are 5 vampires and 7 werewolves available to capture Bella (Kristen Stewart), how many different teams of three comprised of 2 vampires and 1 werewolf can be sent after her? Okay, clearly I know nothing about Twilight because I’m too manly to watch that crap, and I’m pretty sure that’s not how the story goes…but hey…you get the idea.

I’ll follow up with a post with detailed examples to really show you these steps in action.

Combination/Permutation (Counting or Listing) Questions:

STEP 1: Draw out slots, one slot for each item you will ultimately select (NOT how many options are available to you). Label what each slot represents (e.g. Vampire 1, Vampire 2, Werewolf 1).

STEP 2: Fill in each slot with the number of choices/options available for that slot at that precise moment of selection.

STEP 3: Identify and circle each individual pool of choices.

STEP 4: Determine whether the order of picking/choosing items matter or not in each individual pool. Do not worry about the order of picking things at the overall question level, ONLY at the individual pool level.

If ORDER MATTERS –> Multiply all the numbers in slots in that individual pool together, that’s it

If ORDER DOESN’T MATTER–> Multiply all the numbers in the slots in that individual pool together, then divide that product by the number of slots factorial

*To determine if order matters or not, ask yourself is someone will be pissed off if you change around the order. If no one is pissed off, then order doesn’t matter. If someone gets pissed off, then order does matter.

*If there is only one slot in a particular individual pool, who cares if order matters or not because even if you divided by 1! (1 factorial), the result will not change anyways.

STEP 5: Multiply all the individual pool products together. This will get you the final answer. Do not divide anything at this point.

That’s it! Refer back to this post if you ever get lost in the future with these kinds of questions. My follow-up post will walk you through some actual examples to clear things up more. Check back soon.

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