Question

Johnny gets a hamburger for his friend, but forgets to ask what toppings he would want. There are 6 different options. If Johnny gets three toppings how many choices are possible?

Answer 1

Johnny can choose from 20 different combinations of toppings for his friend's hamburger by selecting 3 out of 6 possible toppings using the combination formula C(n, r) = n! / (r! * (n - r)!).

Step-by-step explanation:

Calculating Topping Combinations

Johnny wants to choose 3 toppings for his friend's hamburger out of 6 possible options. The number of possible combinations is calculated using the combination formula, which is defined in mathematics as choosing 'r' items from 'n' options without repetition where the order doesn't matter, and is given by:

C(n, r) = n! / (r! * (n - r)!)

For Johnny's hamburger:

n (the total number of toppings to choose from) = 6

r (the number of toppings Johnny will choose) = 3

Plugging in the values:

C(6, 3) = 6! / (3! * (6 - 3)!)

= (6 * 5 * 4) / (3 * 2 * 1)

= 20 different combinations of toppings.

Therefore, Johnny has 20 different ways to choose toppings for his friend's hamburger.