### 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?

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