How many different menus showing 10 main courses can a restaurant make if it has 15 main courses from which to choose?

The number of ways or different menus containing 10 main courses that the restaurant can make out of the 15 main courses is calculated through the combination.

15C10

This is read as "combination of 15 taken 10" which can be calculated through the equation,

nCr = n! / ((r!) x (n - r) !)

In this item, n is equal to 15 and r is equal to 10.

Substituting the known values to the equation above,

15C10 = 15! / (10!) x (10 - 5) ! = 3003

Thus, there are 3003 different menus that the restaurant can choose from.