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Statistics and Probability Videos 134 videos

SAT Math 1.2 Statistics and Probability
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Combinations 2188 Views


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Description:

A combination is a set of objects in which the order doesn't matter. According to those sandwich artists at Subway, there are over 2,000,000 sandwich combinations available. Although we’re not sure how good the meatball marinara/chicken noodle soup/decaf coffee/oatmeal cookie combination would be.

Language:
English Language

Transcript

00:00

Combinations, a la Shmoop. After a good, long workout at the gym, Clark

00:09

decides that he's earned a hearty meal at ShmoopDonald's as a reward.

00:13

<<ordering>>"One Big Mac, large fries, large Coke, and a baked apple pie, please. Oh, and

00:17

make the Coke "diet." The second Clark gets his food, he feels a

00:20

bit guilty. So he promises himself to only eat two out

00:24

of four of the things he ordered. How many possible combinations of two items

00:29

can Clark have? First of all, a combination is a selection

00:33

of objects in which the order doesn't matter. In Clark's case, it doesn't matter if he has

00:38

the Big shmoop and soda or soda and Big Shmoop... no matter the order, those calories are still

00:46

getting in there. To determine the number of two-item combinations...

00:51

...we can use the following formula: n choose r equals n factorial divided by n minus r

00:59

factorial times r factorial. ...where n is the number of total items we

01:05

have, which in this case is 4... ...and r is the number of items we want in

01:11

a combination. So now let's plug in what we know.

01:18

We get 4 choose 2 equals 4 factorial over 4 minus 2 factorial times 2 factorial.

01:28

Remember... that exclamation mark represents factorial... or the product of an integer

01:35

and all the integers below it. So, 4 factorial equals 4 times 3 times 2 times

01:41

1... which equals 24. Now let's work with the bottom.

01:44

4 minus 2 is 2... 2 factorial is 2 times 1, which is just 2.

01:51

So 2 factorial times 2 factorial is 2 times 2... which is just 4.

01:56

24 divided by 4 is 6. So the number of 2-item combinations Clark can have is...6!

02:11

Clark may still be erasing much of his hard work at the gym...

02:14

...but at least he'll be giving his jaw muscles

02:31

a workout.

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