From a group of 6 employees, k employees are chosen to be on the party

Target question: What is the value of k?

Given: From a group of 6 employees, k employees are chosen to be on the party-planning committee.
So, k can equal 1, 2, 3, 4, 5, or 6

Since the order of the selected employees does not matter, we can use combinations.
We can choose k employees from 6 employees in 6Ck ways.
Let's take a moment to calculate the combinations (which we can do quickly in our head - see the video below)
6C1 = 6
6C2 = 15
6C3 = 20
6C4 = 15
6C5 = 6
6C6 = 1

Statement 1: k is a prime number
So, k can equal 2, 3, or 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: There are 15 different ways to create the party-planning committee consisting of k employees.
We already saw that 6C2 = 15 AND 6C4 = 15
This means k = 2 OR k = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that k = 2 OR k = 3 OR k = 5
Statement 2 tells us that k = 2 OR k = 4
Since both statements must be true, and since k = 2 is the ONLY k-value that is shared by both statements, we can conclude that k = 2
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer:
RELATED VIDEOS