Question

A Cafeteria offers 6 sandwich choices,5 desserts, and 3 beverages

How many different meals consisting of 1sandwich,1 dessert and 1 beverage can be ordered?

Answer 1

Here, we are sampling 1 of 6 sandwiches, 1 of 5 desserts and 1 of 3 beverages in any order. The easiest way to do this is to use the 'choose' function on a calculator.

If we had 'n' objects and wanted to know many ways there were of choosing 'k' of these (without replacing any object we've picked and choosing them in no particular order), then we would solve:
\[\left(\begin{matrix}n \\ k\end{matrix}\right)\] ("n choose k"), which is also equal to \[\frac{ n! }{ k!(n-k)! }\]
where n! is "n factorial", or all the values from n down to 1 multiplied together
(n! = (n)(n-1)(n-2)....(1)). In using either of these methods, it is much simpler to work them out on a scientific calculator.

So, as we are sampling 1 of 6 sandwiches AND 1 of 5 desserts AND 1 of 3 beverages, the number of different meals is:
\[\left(\begin{matrix}6 \\ 1\end{matrix}\right)\] multiplied by\[\left(\begin{matrix}5 \\ 1\end{matrix}\right)\] multiplied by
\[\left(\begin{matrix}3 \\ 1\end{matrix}\right)\] giving us an answer of 90 different meals.