A catering service offers 7 appetizers, 3 main courses, and 5 desserts. A customer is to select 4 appetizers, 2 main courses, and 4 desserts for a banquet. In how many ways can this be done?

This question is based on combinations

Out of 7 appetizers, 4 are to be selected, this becomes = 7C4

Out of 3 main courses, 2 are to be selected, this is = 3C2

Out of 5 desserts, 4 are to be selected, this is = 5C4

So, total ways become =

7C4 * 3C2 * 5C4

7!/4! (7-4) ! * 3!/2! (3-2) ! * 5!/4! (5-4) !

= 35*3*5 = 525 ways

Hence, this can be done in 525 ways.