Question

The cafeteria manager can choose from among six I dishes for the lunch menu apple sauce broccoli corn dumplings eggrolls or french fries

Answer 1

full question: (please post this next time)

A cafeteria manager can choose from among six side dishes for the lunch menu: applesauce, broccoli, corn, dumplings, egg rolls, or French fries. He uses a computer program to randomly select three dishes for Monday’s lunch. What is the theoretical probability that applesauce and broccoli will both be offered on Monday? a. 10% b. 20% c. 50% d. 80%

Answer 2

first calculate the # of combinations that have both applesauce and broccoli, along with a third item. the applesauce and broccoli are given, so for the third item, there are only 4 possibilities left:

applesauce + broccoli + corn
applesauce + broccoli + dumplings
applesauce + broccoli + egg rolls
applesauce + broccoli + french fries

so the numerator of our final expression will be 4

now, to determine the denominator, we need to find out how many total menu combinations there are

the order doesn't matter (all the side dishes get served at once, so there's no "order")

therefore, use the combination formula nCr to determine the number of possible menus of 3 items made from 6 choices
in this case, n = 6 since there are 6 items to choose from, and r = 3 since 3 menu items ar ebeing chosen at once

from there, simply calculate (# of combinations with apple sauce + broccoli) / (total # of combinations)