Question

a chef randomly chooses 5 apples from a case of 24 apples. which best

1. represents the number of ways the chef can make the selection?

a ( _ { 5 } c _ { 19 } )
b ( _ { 24 } c _ { 5 } )
c ( _ { 5 } p _ { 24 } )
d ( _ { 19 } p _ { 5 } )

Explanation:

Step1: Determine the type of selection

Since the order of choosing apples does not matter (it's just a selection of 5 apples out of 24), we use the combination formula \(_{n}C_{r}=\frac{n!}{r!(n - r)!}\), where \(n\) is the total number of items and \(r\) is the number of items to be chosen.

Step2: Identify \(n\) and \(r\) values

Here, \(n = 24\) (total number of apples) and \(r=5\) (number of apples to be chosen).

Answer:

B. \(_{24}C_{5}\)