Question

Lauri is planning a bridal shower for her best friend. At the party , she wants to serve 3 beverages, 2 appetizers, and 2 desserts, but she does not have time to cook. She can choose from 18 bottled drinks,8 frozen appetizers, and 5 prepared dessertsat the supermarket. How many different ways can Lauri pick the food and drinks to serve at the bridal shower?

Answer 1

In order to calculate the probability of each item, we need to use a combination formula.

The combination of n choose p elements can be calculated with the formula below:

$C(n,p)=\frac{n!}{p!(n-p)!}$

For the beverages, she will choose 3 items among 18 options, so the number of ways she can choose is:

$C(18,3)=\frac{18!}{3!15!}=\frac{18\cdot17\operatorname{\cdot}16}{3\operatorname{\cdot}2}=816$

For the appetizers, she wants 2 items among 8 options, so:

$C(8,2)=\frac{8!}{2!6!}=\frac{8\operatorname{\cdot}7}{2}=28$

For the desserts, she will choose 2 items from 5 options, so:

$C(5,2)=\frac{5!}{2!3!}=\frac{5\operatorname{\cdot}4}{2}=10$

Now, calculating the total number of possibilities, we have:

$\begin{gathered} N=C(18,3)\operatorname{\cdot}C(8,2)\operatorname{\cdot}C(5,2)\\ \\ N=816\operatorname{\cdot}28\operatorname{\cdot}10\\ \\ N=228480 \end{gathered}$