### Home > A2C > Chapter 10 > Lesson 10.2.6 > Problem 10-145

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? Homework Help ✎

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

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

_{6}*C*_{3}

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

2 · _{6}*C*_{2}

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

_{6}*C*_{1}

_{6}*C*_{3} + 2 · _{6}*C*_{2} + _{6}*C*_{1} = 20 + 2(15) + 6 = 56