Justin has
7
CDs that he is going to give away. He lets his best friend choose
2
of the
7
CDs. How many different groups of
2
CDs are possible?
combinations of 2 of 7 because order does not matter
7!/[ 2! (7-2)! ]
7!/(2*5!)
7*6/2
21
To find out how many different groups of 2 CDs are possible, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / [(r!)(n-r)!],
where n is the total number of items and r is the number of items chosen.
In this case, Justin has 7 CDs, and he is going to give away 2 of them. So, we need to find C(7, 2) to determine the number of possible groups.
Using the formula:
C(7, 2) = 7! / [(2!)(7-2)!]
= 7! / (2!)(5!)
= (7 x 6 x 5!) / (2!)(5!)
= (7 x 6) / (2 x 1)
= 42 / 2
= 21.
Therefore, there are 21 different groups of 2 CDs that Justin's best friend can choose from the 7 CDs.