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 =[tex]\frac{n!}{(n-r)!r!}[/tex]
So, The number of 2 topping sandwiches= 5 C 2 =[tex]\frac{5!}{(5-2)!2!}[/tex]
The number of 2 topping sandwiches=[tex]\frac{5!}{(3)!2!}[/tex]
The number of 2 topping sandwiches=[tex]\frac{(5*4*3*2*1)}{(3*2*1)(2*1)}[/tex]
The number of 2 topping sandwiches=[tex]\frac{120}{12}[/tex]
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
