Question

Sana throws a pizza party. She has ordered different pizzas which include, 8 Chicken pizzas, 10 Vegetable pizzas and 12 Beef pizza from different restaurants.
a) If she wants to serve 3 Chicken pizzas and serving order is important, how many ways are there to do this
b) If 6 pizzas are to be randomly selected from the 30 pizzas already available, how many ways are there to do this?

Answer 1

Given that,

Chicken pizzas = 8

Vegetable pizzas = 10

Beef pizzas = 12

(a). If she wants to serve 3 Chicken pizzas and serving order is important,

We need to calculate the number of ways

Using formula of permutations

$P(n,r)=\dfrac{n!}{(n-r)!}$

Where, n =  total number of items,

r =  number of items being chosen at a time

Put the value into the formula

$P(8,3)=\dfrac{8!}{(8-3)!}$

$P(8,3)=336$

(b). If 6 pizzas are to be randomly selected from the 30 pizzas already available,

We need to calculate the number of way

Using formula of combination

$^{n}C_{r}=\dfrac{n!}{r!(n-r)!}$

Where, n =  total number of items,

r =  number of items being chosen at a time

Put the value into the formula

$^{30}C_{6}=\dfrac{30!}{6!(30-6)!}$

$^{30}C_{6}=593775$

Hence, (a). The number of ways will be 336.

(b). The number of ways will be 593775.