Question

A sandwich shop offers the following toppings. How many two topping sandwiches can you make?

-lettuce
-tomato
-bacon
-cheese
-mustard

Answer 1

You can make 20 two topping sandwiches.

Answer 2

A sandwich shop offers the following toppings. How many two topping sandwiches can you make?

-lettuce

-tomato

-bacon

-cheese

-mustard

Solution:

There are five toppings available and the five toppings are lettuce, tomato, bacon, cheese, mustard.

We need to make 2 topping sandwiches.

So, we can select any 2 toppings from the available 5 toppings

So, we must use combination here

So, the number of two topping sandwiches is 5 combination 2

Or, Number of 2 topping sandwiches= 5 C 2

The formula is, n C r =
`(n!)/((n-r)!r!)`

So, The number of 2 topping sandwiches= 5 C 2 =
`(5!)/((5-2)!2!)`

The number of 2 topping sandwiches=
`(5!)/((3)!2!)`

The number of 2 topping sandwiches=
`((5*4*3*2*1))/((3*2*1)(2*1))`

The number of 2 topping sandwiches=
`(120)/(12)`

The number of 2 topping sandwiches=10

that is,

lettuce, tomato(1)

lettuce, bacon(2)

lettuce, cheese(3)

lettuce, mustard(4)

tomato,bacon(5)

tomato,cheese(6)

tomato,mustard(7)

bacon,cheese(8)

bacon, mustard(9)

cheese,mustard(10)

Answer: So, there are 10 possible two topping sandwiches