ShmoopTube

00:02

Okay sy match members last section in this lovely exam

00:06

Ok well here we go What would we need to

00:08

use to find the number of ways we could pick

00:10

three toppings for a pizza given ten choices Yeah all

00:20

right Well when we're picking a smaller group from a

00:22

larger one like the three toppings we want from that

00:25

ten topping choices were often trying to determine how many

00:28

ways we can pick the smaller group The issue we

00:31

have to deal with before we can find the actual

00:33

different number of ways to choose our smaller group is

00:36

whether the order we choose the items in the smaller

00:40

group matters like think about it If you were picking

00:43

from a deck of cards the size of that debt

00:45

goes from fifty two to fifty one fifty forty nine

00:48

so the odds then change on the margin each time

00:50

you make a pick So if the order we picked

00:53

the items in this problem in the smaller group matters

00:56

will end up with loads more options than we will

00:58

then if the order doesn't matter if order does matter

01:02

like we chose pepperoni green olives and pineapple as our

01:05

three well we can also choose green olives pepperoni and

01:09

pineapple or pineapple green olives and pepperoni And so on

01:13

each of those different ordering sze of the same three

01:16

ingredients would be a whole new option We call these

01:19

permutations the shortcut simple is npr where n is the

01:24

size of the large group and our is the size

01:27

of the smaller group and p is well just probability

01:31

of what's going on there If order doesn't matter well

01:34

then we just get the one option with those three

01:36

toppings To get a new option we'd need to toss

01:38

out a topping the pineapple get rid of that on

01:40

a pizza what they're doing and replace it with something

01:43

else like black olives Yeah we call these combinations The

01:46

shortcut symbol is n c r where ends the size

01:49

of the large group and ours the size of the

01:52

small group it's pretty clear order doesn't matter in this

01:55

case as it doesn't matter if we choose pepperoni before

01:58

green olives or after they all end up in the

02:01

same slice and you know in the same place since

02:04

this is a combination will need the symbol ten c

02:07

three to represent all of our different three items pizzas

02:11

so that's it that's the answer at sea Ten c

02:13

three

Full Transcript