A sandwich shop offers the following toppings. How many two-topping sandwiches can you make?
lettuce
tomato
bacon
cheese
mustard
A. 8
B. 10
C. 12
D. 20.
D. 20.
To find the answer, we need to use combinations (since order does not matter for the two-topping sandwiches). The formula for combinations is:
nCr = n! / r!(n-r)!
where n is the total number of items (in this case, toppings) and r is the number of items we need to choose (in this case, 2 toppings).
Plugging in our numbers, we get:
6C2 = 6! / 2!(6-2)! = 15
So there are 15 different combinations of two toppings.
To find out how many two-topping sandwiches you can make, you need to calculate the number of combinations. Since you're choosing two toppings from a total of five options, you can use the combination formula, which is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of options and r is the number of options you're choosing.
In this case, you have 5 options (lettuce, tomato, bacon, cheese, and mustard) and you're choosing 2 toppings.
Plugging the values into the formula:
5C2 = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3 * 2!)/[(2!)(3 * 2!)]
= (5 * 4)/(2 * 1)
= 20/2
= 10
Therefore, you can make 10 two-topping sandwiches.
The correct answer is B. 10.