Question

Can you please help me with number 34. Determine the number of ways that each can occur

Answer 1

You need to determine the number of possible combinations when you choose 4 appetizers out of 11 options in the dinner menu. Assuming that you are not going to repeat appetizers, to determine this number you have to apply combinations, using the formula:

`C(n,r)=(n!)/(r!(n-r)!)`

Where

n is the number of options available

r is the number of options you have to choose, with no repetition, and the order doesn't matter.

For this exercise:

n=11

r=4

The combination can be determined as follows:

`\begin{gathered} C(11,4)=(11!)/(4!(11-4)!) \\ C(11,4)=(11!)/(4!\cdot7!) \\ C(11,4)=(39916800)/(24\cdot5040) \\ C(11,4)=330 \end{gathered}`

There are 330 combinations possible to choose 4 out of 11 appetizers from the menu.