Juan has eight CDs that he is going to give away he lets his best friend choose two of the eight CDs how many different groups of cds are possible?
To find the number of different groups of CDs that are possible when Juan lets his best friend choose two out of the eight CDs, we can use the concept of combinations.
In combinatorics, the number of combinations is calculated using the formula:
C(n, r) = n! / (r!(n-r)!),
where n represents the total number of items or options available, and r represents the number of items or options to be chosen.
In this case, Juan has 8 CDs and wants to choose 2 of them, so we have n = 8 and r = 2.
Applying the formula, we get:
C(8, 2) = 8! / (2!(8-2)!)
= (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 6 * 5 * 4 * 3 * 2 * 1)
= (8 * 7) / (2 * 1)
= 56 / 2
= 28.
Therefore, there are 28 different groups of CDs possible when Juan lets his best friend choose two out of the eight CDs.