Acatering service offers 8 appetizers, 11 main courses, and 4 desserts. a banquet chairperson is to select 5 appetizers, 9 main courses, and 2 desserts for a banquet. in how many ways can this be done?

is the formula that calculates the total number of ways that r objects can be selected out of n.

where r!=1*2*3*...*(r-1)*r

for example 

is the total number of ways we can pick 5 objects out of 8.

similarly 





This means that there are 56 ways of picking the appetizers, 55 ways of picking the main courses and 6 ways of picking the desserts.

Since any of the selections of the different meals, can be combined with any selections of the other 2 meals, there are :

56*55*2=6160 ways, of selecting the 3 types of meals.

6160