Question

How many different menus can be made showing 5 main courses from 15 choices?

A. 72,072


B. 12,012


C.3,003

Answer 1

3,003 different menus can be made showing 5 main courses from 15 choices

Explanation:

we need to find how many different menus can be made showing 5 main courses from 15 choices

Total of 15 choices

5 to be selected from 15 choice

'r' is selected from n choices in nCr ways

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

Here 5 is selected from 15 in 15C5 ways

`15C5= (15!)/(5!(15-5)!)\\15C5= (15!)/(5!(10)!)=3003`

So 3,003 different menus can be made showing 5 main courses from 15 choices