# TSI Math: Using Combinations to Select Pizza Toppings

What would we need to use to find the number of ways we could pick 3 toppings for a pizza given 10 choices?

Data Analysis, Statistics, and Probability | Probabilistic Reasoning |

Mathematics and Statistics Assessment | Probabilistic Reasoning |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Data Analysis, Statistics, and Probability |

TSI Mathematics | Data Analysis, Statistics, and Probability |

Test Prep | TSI |

### Transcript

larger one like the three toppings we want from that

ten topping choices were often trying to determine how many

ways we can pick the smaller group The issue we

have to deal with before we can find the actual

different number of ways to choose our smaller group is

whether the order we choose the items in the smaller

group matters like think about it If you were picking

from a deck of cards the size of that debt

goes from fifty two to fifty one fifty forty nine

so the odds then change on the margin each time

you make a pick So if the order we picked

the items in this problem in the smaller group matters

will end up with loads more options than we will

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

like we chose pepperoni green olives and pineapple as our

three well we can also choose green olives pepperoni and

pineapple or pineapple green olives and pepperoni And so on

each of those different ordering sze of the same three

ingredients would be a whole new option We call these

permutations the shortcut simple is npr where n is the

size of the large group and our is the size

of the smaller group and p is well just probability

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

then we just get the one option with those three

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

out a topping the pineapple get rid of that on

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

else like black olives Yeah we call these combinations The

shortcut symbol is n c r where ends the size

of the large group and ours the size of the

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

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

green olives or after they all end up in the

same slice and you know in the same place since

this is a combination will need the symbol ten c

three to represent all of our different three items pizzas

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

three