Final answer:
To select 6 DVDs from 200, use the combination formula C(n, k) = n! / (k!(n-k)!), where n is 200 and k is 6. The answer is derived from combinatorics and results in choosing 6 out of 200 DVDs in many different ways. Due to large factorials involved, a calculator or computer is typically used for calculation.
Step-by-step explanation:
To determine how many ways you can select 6 free DVDs from a list of 200 DVDs, you use combinations since the order in which you select the DVDs does not matter. This is a situation related to combinatorial mathematics. To calculate the number of combinations, you can use the formula for combinations:
C(n, k) = n! / (k!(n-k)!), where
- n is the total number of items to choose from (200 DVDs), and
- k is the number of items to choose (6 DVDs).
Substituting the values into the formula, we get:
C(200, 6) = 200! / (6!(200-6)!) = 200! / (6! * 194!)
The calculation involves factorials, which are too large to compute manually, but a calculator or a computer can handle such large numbers to give us the answer.
The details provided in the reference information about video rental stores and the related keyword 'probability distribution' do not affect the calculation of combinations and are therefore not needed to answer this question.