CPM Homework Help : A2C Problem 10-145

Jean Luc's favorite Asian restaurant has six dishes on its lunch menu. He wants to get their three-item combo for lunch and is reminded by the counter-person that he can order two or three servings of the same selection. How many different ways could he order lunch?

Hint:

The order in which the food is selected does not matter.

Step 1:

For a three item lunch, how many items are there to choose from and how many are you going to select?

₆C₃

Step 2:

Now find how many lunches of two items can be selected.

2 · ₆C₂

Step 3:

Now find how many lunches of one item can be selected.

₆C₁

Answer:

₆C₃ + 2 · ₆C₂ + ₆C₁ = 20 + 2(15) + 6 = 56