Questions: A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected? A Combination B Permutation C Counting Principle

Solution Steps

To determine the number of ways to select 6 people out of 13, we need to use combinations because the order in which the people are selected does not matter.

1. Identify the total number of volunteers (n = 13).
2. Identify the number of people to be selected (r = 6).
3. Use the combination formula \( C(n, r) = \frac{n!}{r!(n-r)!} \) to calculate the number of ways to select 6 people from 13.

We have a total of \( n = 13 \) volunteers and we need to select \( r = 6 \) people for the test.

To find the number of ways to select 6 people from 13, we use the combination formula: \[ C(n, r) = \frac{n!}{r!(n-r)!} \] Substituting the values, we have: \[ C(13, 6) = \frac{13!}{6!(13-6)!} = \frac{13!}{6! \cdot 7!} \]

Calculating \( C(13, 6) \): \[ C(13, 6) = \frac{13 \times 12 \times 11 \times 10 \times 9 \times 8}{6 \times 5 \times 4 \times 3 \times 2 \times 1} = 1716 \]

Final Answer