A catering service offers 12 appetizers, 4 main courses, and 8 desserts. A banquet chairperson is to select 9 appetizers, 2 main courses, and 7 desserts for a banquet. In how many ways can this be done
We know this is a combination with no repeats, because order does not matter. This is the formula for that: [tex] \frac{n!}{r!(n-r)!} [/tex] (n is the number you have to choose from, and r is the amount you are choosing) To make this go faster, I'll be doing all the work on paper and insert a photo of it. The first part of this is me going through the work. I used a calculator to assist with multiplication and division. We'll now find out how many different combinations can be made in total. See my paper to see what I do. The rest of my answer is listed there.
