Question

Rita is selecting a sandwich at the deli. The deli has four types of meat, three types of cheese and two types of bread. A deluxe sandwich consists of exactly one meat type, two different types of cheese and one bread type. How many different deluxe sandwich combinations are possible

Answer 1

Answer:

24

Step-by-step explanation:

I did Mathcounts

Answer 2

Answer:

24 possible dishes

Step-by-step explanation:

Given

Total

$Meat = 4$

$Cheese = 3$

$Bread = 2$

Selection

$Meat = 1$

$Cheese =2$

$Bread = 1$

Required

Determine the number of possible combo

Rita wants to select 1 of 4 meat types,

So, the number of selections is: $^4C_1$

Rita wants to select 2 of 3 cheese types,

So, the number of selections is: $^3C_2$

Rita wants to select 1 of 2 cheese types,

So, the number of selections is: $^2C_1$

The total number of selections is:

$Total = ^4C_1 * ^3C_2 * ^2C_1$

Using

$^nC_r = \frac{n!}{(n-r)!r!}$

We have:

$Total = \frac{4!}{(4-1)!1!} * \frac{3!}{(3-2)!2!} * \frac{2!}{(2-1)!1!}$

$Total = \frac{4!}{3!1!} * \frac{3!}{1!2!} * \frac{2!}{(1!1!}$

$Total = \frac{4*3!}{3!*1} * \frac{3*2!}{1*2!} * \frac{2*1}{1*1}$

$Total = 4* 3 * 2$

$Total = 24$

Hence, there are 24 possible dishes