Final answer:
To determine the number of ways the manager can choose 8 posters from 27, we use the formula for combinations. The answer is calculated as C(27, 8), which simplifies to 27! divided by the product of 8! and 19!. This calculation reveals the total number of combinations possible.
Step-by-step explanation:
The question is asking about the number of combinations possible when choosing 8 game posters out of 27 for a promotional giveaway. This is a problem of combinatorics, which is a part of discrete mathematics. The formula for combinations is given by:
C(n, k) = n! / (k!(n-k)!)
where C(n, k) represents the number of combinations, n represents the total number of items to choose from, and k represents the number of items to choose. In this case, we have:
C(27, 8) = 27! / (8!(27-8)!) = 27! / (8!19!)
To calculate this without expanding the factorials entirely, we can cancel out common factors. The answer will provide us with the number of ways the manager can choose 8 game posters from a total of 27 for the promotion.