In a shipment of 18 smartphones, 2 are defective. How many ways can a quality control inspector randomly test 5 smartphones, of which 2 are defective?
To find the number of ways the quality control inspector can randomly test 5 smartphones, of which 2 are defective, we can use combinatorics.
The combinatorial formula we can use is called "combinations". The formula for combinations (also known as nCr) is:
nCr = n! / (r! * (n-r)!)
Where:
n = Total number of items
r = Number of items chosen or selected
In this case:
n = Total number of smartphones (18)
r = Number of defective smartphones (2)
So, to find the number of ways the quality control inspector can randomly test 5 smartphones, of which 2 are defective, we can calculate 18C5 * 2C2.
The calculation would be as follows:
18C5 = 18! / (5! * (18-5)!)
= (18 * 17 * 16 * 15 * 14) / (5 * 4 * 3 * 2 * 1)
= 8568
2C2 = 2! / (2! * (2-2)!)
= 1
Therefore, the number of ways the quality control inspector can randomly test 5 smartphones, of which 2 are defective, is 8568 * 1 = 8568 ways.