Question

a restaurant sells pizzas there are 3 different crusts 8 different toppings and 3 different cheeses how many combinations of one toppiong pizzas are possible?
A) 72
B) 67
C) 75

Answer 1

Answer:

168

Step-by-step explanation:

Cheese :  

3

choices

Toppings :  

8

choices for the first,  

7

for the second and  

6

for the third, a total of  

8

×

7

×

6

=

336

, IF the order of toppings were important -- which it isn't. This number is called the number of permutations .

Three things can be ordered in 6 ways (try this), so in the 336 permutations, there are groups of 6 that amount to the same combination :

123=132=213=231=312=321, etc.

So we have to divide the number of permutations by the number of orders to reach the number of combinations:

There are thus 336 : 6 = 56 possibilities for the toppings.

Since we need cheese AND toppings we multiply:

Number of different pizzas: 3 x 56 = 168.

Calculator : if you have the nCr function the answer would be:

3 x 8 nCr 3 = 168