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

24

Explanation:

I did Mathcounts

Answer 2

24 possible dishes

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 = (n!)/((n-r)!r!)`

We have:

`Total = (4!)/((4-1)!1!) * (3!)/((3-2)!2!) * (2!)/((2-1)!1!)`

`Total = (4!)/(3!1!) * (3!)/(1!2!) * (2!)/((1!1!)`

`Total = (4*3!)/(3!*1) * (3*2!)/(1*2!) * (2*1)/(1*1)`

`Total = 4* 3 * 2`

`Total = 24`

Hence, there are 24 possible dishes