Question

A friend of mine is giving a dinner party. His current wine supply includes 8 bottles of zinfandel, 10 of merlot, and 9 of cabernet, all from different wineries. If 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety?

Answer 1

This problem can be simply solved by calculating for the product of each combination of each wine. There are 8C2 ways to pick from 8 bottles of zinfandel, 10C2 ways to pick from merlot and 10C9 ways to pick from cabernet.

Total number of ways = 8C2 * 10C2 * 9C2

Total number of ways = 45,360

Answer 2

For this problem, we use the formula for combination. When the notation is written as nCr, that is equivalent to the equation below:

nCr = n!/r!(n-r)!
where
n is the total number of objects
r is the number of one type of object

Using the fundamental counting principle, we multiple each nCr equation for each type of bottle. The solution is:

Number of ways = 8C2×10C2×9C2 = 45,360 ways