Question

The "eating club" is hosting a make-your-own sundae at which the following are provided:

Ice Cream Flavors:
Chocolate,Cookies 'n' cream,Strawberry,Vanilla.
Toppings: Caramel,Hotfudge,Marshmallow,M&M's,Nuts,Strawberries.

(a) How many sundaes are possible using one flavor of
ice cream and three different toppings?
(b) How many sundaes are possible using one flavor of
ice cream and from zero to six toppings?
(c) How many different combinations of flavors of three
scoops of ice cream are possible if it is permissible to
make all three scoops the same flavor?

Answer 1

In part (a), there are 80 sundaes possible using one flavor of ice cream and three different toppings. In part (b), there are 64 sundaes possible using one flavor of ice cream and from zero to six toppings. In part (c), there are 4 different combinations of flavors of three scoops of ice cream.

Step-by-step explanation:

(a) To calculate the number of sundaes possible using one flavor of ice cream and three different toppings, we can use the concept of combinations. There are 4 ice cream flavors and we can choose 1 of them. There are 6 toppings available and we need to choose 3 of them. The number of sundaes is given by the formula C(4,1) * C(6,3) = 4 * 20 = 80 sundaes.

(b) To calculate the number of sundaes possible using one flavor of ice cream and from zero to six toppings, we can sum up the number of sundaes for each possible number of toppings. Using the same formula as in part (a), the number of sundaes for each number of toppings is: C(6,0) + C(6,1) + C(6,2) + C(6,3) + C(6,4) + C(6,5) + C(6,6) = 1 + 6 + 15 + 20 + 15 + 6 + 1 = 64 sundaes.

(c) To calculate the number of different combinations of flavors of three scoops of ice cream, we can use combinations again. There are 4 ice cream flavors and we can choose 3 of them. The number of combinations is given by the formula C(4,3) = 4.