Question

Pizza Paradise offers 4 types of crust, 10 toppings, and 8 kinds of cheese for the mega calzone. How many different mega calzones can be made if a mega calzone contains 3 different toppings and 3 different cheeses

Answer 1

Answer:

26880 ways

Step-by-step explanation:

Given

$Crust = 4$

$Toppings = 10$

$Cheese = 8$

Required

Determine the number of ways 3 toppings and 3 cheese can be selected

The number of crusts to be selected was not stated. So, I'll assume 1 crust to be selected from 4.

This can be done in $^4C_1$ ways

For the toppings:

3 can be selected from 10 in $^{10}C_3$ ways

For the cheeses:

3 can be selected from 8 in $^{8}C_3$ ways

Total number of selection is:

$Total = ^4C_1 * ^{10}C_3 * ^{8}C_3$

Apply combination formula:

$Total = \frac{4!}{(4-1)!1!} * \frac{10!}{(10-3)!3!} * \frac{8!}{(8-3)!3!}$

$Total = \frac{4!}{3!1!} * \frac{10!}{7!3!} * \frac{8!}{5!3!}$

$Total = \frac{4*3!}{3!*1} * \frac{10*9*8*7!}{7!*3*2*1} * \frac{8*7*6*5!}{5!*3*2*1}$

$Total = \frac{4}{1} * \frac{10*9*8}{3*2*1} * \frac{8*7*6}{3*2*1}$

$Total = 4 * \frac{720}{6} * \frac{336}{6}$

$Total = 4 * 120* 56$

$Total = 26880$

Hence, there are 26880 ways