A caterer offers 24 different types of desserts. In how many ways can 5 of them be chosen for a banquet if the order doesn’t matter?

Question

A caterer offers 24 different types of desserts. In how many ways can 5 of them be chosen for a banquet if the order doesn’t matter?

Answer 1

Since the order doesn't matter in this case, this is a combination problem (as opposed to a permutation problem, where the order matters). Therefore, you would use the combination formula: _nC_r= (n!) / r !(n-r)!, where n represents the number of total things in the set, and r is the number of things of chosen at a time.

So if we substitute for the variables: _nC_r= (n!) / r !(n-r)! --> _nC_r= (24!) / 5! (24-5)!, which gives us 42,504 different combinations.

Answer 2

You will be looking at combinations with the notation C(n, k), where n is the number of desserts in total and k is the number of desserts selected for a banquet.

C(24, 5) = 24! ÷ [(5)!*(19)!] = 42,504

There are 42,504 possible ways to select 5 desserts for a banquet when order doesn't matter.