Finding probability using combinations

Intro

Howdy!  I'm Professor Curtis of Aspire Mountain Academy here with more statistics homework help.  Today we're going to learn how to find probability using combinations.  Here's our problem statement: When testing for current in a cable with 10 color coded wires, the author used a meter to test three wires at a time.  How many different tests are required for every possible pairing of three wires?

Solution

OK, so we've got a total amount that we're taking a portion at a time.  So we could be calculating permutations, or we could be calculating combinations.  The way we tell the difference is we ask the key question: Is the order important?  Does the order matter?  Here the order does not matter.

You know, if you pick, say, the red wire, the white wire, and the blue wire, and you hook them up to the meter, you're going to get the same result from the meter if you select the red, the white, and, you know --- what was that other color I selected?  Yeah.  Was it black?  Yeah, I just had a brain fart. Anywho, yeah, you just — it doesn't matter what the order is, you hook them up to the same three wires, you hook them up to the meter electrically, they're going to perform the same.  So there is no difference with the order.  The order is therefore not important.  Because the order's not important, we're going to use combinations.

Now typically you're going to be selecting combinations with your calculator.  You'll punch it out on your calculator.  We don't have --- the calculator that I have here on my computer doesn't have a combination or permutation function.  So I'm going to a website, calculator.net, and let's bring that down a little bit so you can see here calculator.net.  And there's all kinds of calculators here.  And the one I'm selecting is for permutations and combinations.  The nice thing about this is that it just punches everything out for you.  You're probably not going to be able to use this on a test, but if you learn how to use your calculator, it'll perform the same function for you.  You just got to get the same numbers here.

The total amount that we're testing —  there's 10 wires total, so we'll put 10 here.  And then the amount in each subset — how many are we taking at a time?  Here it says we're testing three at a time, so I'm just going to put 3.  And notice it calculates both the permutations and the combinations for you.  We want combinations because the order is not important.  So we're going to select the 120.  Excellent!

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