Answer: The required number of ways is 46200.
Step-by-step explanation: Given that a catering service offers 8 appetizers, 11 main courses, and 7 desserts.
A banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts.
We are to find the number of ways in which this can be done.
We know that
From n different things, we can choose r things at a time in ways.
So,
the number of ways in which 7 appetizers can be chosen from 8 appetizers is
the number of ways in which 8 main courses can be chosen from 11 main courses is
and the number of ways in which 4 desserts can be chosen from 7 desserts is
Therefore, the number of ways in which the banquet committee is to select 7 appetizers, 8 main courses, and 4 desserts is given by
Thus, the required number of ways is 46200.