Question

A catering service offer 3 appetizer, 10 main courses and 4 desserts. A costumer is to select 2 appetizer 4 main course and 2 desserts for a banquet in how many ways can this be done

Answer 1

The costumer has to choose 2 out of 3 appetizers, 4 out of 10 main courses and 2 out of 4 desserts.

For each of these choices, there are

$\displaystyle \binom{3}{2}=3,\quad \binom{10}{4}=210,\quad \displaystyle \binom{4}{2}=6$

possible choices.

So, the costumer has a total of

$3\cdot 210 \cdot 6=3780$

possible choices.