Question

If an Italian restaurant offers 5 different toppings to put on pizzas how many different pizzas can be prepared? NOTE: assume the restaurant also prepares pizza with no toppings.

Answer 1

5!

Answer 2

do u have the choices ?

Answer 3

16 31 25 32

Answer 4

Hint:

Number of ways = (number of ways with 5 toppings) + (number of ways with 4 toppings) + (number of ways with 3 toppings) + (number of ways with 2 toppings) + (number of ways with 1 toppings) + (number of ways with 0 toppings)

Answer 5

16?

Answer 6

so you're adding

5 C 5 + 5 C 4 + 5 C 3 + 5 C 2 + 5 C 1 + 5 C 0

you might notice that these numbers can be found in pascals triangle and they add up to some power of a whole number

Answer 7

5+4+3+2+1+1= 16

Answer 8

not quite

Answer 9

there is 5 C 5 = 1 way to order a pizza with 5 toppings

there are 5 C 4 = 5 ways to order a pizza with 4 toppings

there are 5 C 3 = 10 ways to order a pizza with 3 toppings

etc etc

add them all up

Answer 10

32?

Answer 11

yep, a short cut is to look at pascals triangle and you'll see a row starting with 1, 5, 10, ...

add those numbers up to get

1+5+10+10+5+1 = 32

Answer 12

awesome thanks!

Answer 13

an even bigger shortcut is to use the idea that the answer is 2^n where n = number of toppings you can choose from

so 2^5 = 32

Answer 14

oh i see