Question 665627
The answer is the number of Combiations you can have by choosing a group of 18 from a total population of 23.
(1) 23C18 is the symbol we use, it is evaluated as
(2) 23C18 = 23!/((23-18)!*18!) or
(3) 23C18 = 23!/(5!*18!)
Using your calculator (find the ! key for factorial) to get
(4) 23C18 = 33,649,. If you don't have ! key (3) simplifies to
(5) 23C18 = (23*22*21*20*19)/120
You also want to know about a caterer picking meal.
For the appitizers we have 3C2 = 3
For the main dish we have 11C7 = 11!/94!7!) = 330
For dessert we have 4C2 = 6
The total number of choices is 3*330*6 = 5940