Miguel has
6
CDs that he is going to give away. He lets his best friend choose
3
of the
6
CDs. How many different groups of
3
CDs are possible?
Bobpursley showed you how to solve a similar problem. Please apply what you learned from him to this problem. Someone will be glad to check your answer.
To find the number of different groups of 3 CDs that Miguel's best friend can choose from the 6 CDs, we can use the concept of combination.
In combination, the order of the items doesn't matter, and we only care about selecting a certain number of items from a larger set.
The formula for combinations is given by:
nCr = n! / (r! * (n - r)!)
Where n represents the total number of items, and r represents the number of items we want to choose.
In this case, we have 6 CDs, and we want to choose 3 of them. Plugging these values into the formula:
6C3 = 6! / (3! * (6 - 3)!)
Simplifying further:
6C3 = 6! / (3! * 3!)
Now, let's calculate:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
3! = 3 * 2 * 1 = 6
Plugging these values back into the formula:
6C3 = 720 / (6 * 6)
Simplifying further:
6C3 = 720 / 36
Calculating the final result:
6C3 = 20
Therefore, there are 20 different groups of 3 CDs that Miguel's best friend can choose from the 6 CDs.