Chris is shopping for CDs and decides to purchase 3 movie soundtracks. The store has 9 different movie sountracks in stock. How many different selections of movie sountracks are possible?
this is just a simple combination: C(9,3) = 9!/(3!6!) = 9*8*7/3! = 84
To find the number of different selections of movie soundtracks that Chris can purchase, we need to use the concept of combinations.
In this case, Chris wants to purchase 3 movie soundtracks out of the 9 different options available in the store. To calculate the number of possible selections, we can use the formula for combinations:
C(n, r) = n! / (r! * (n - r)!)
In this formula, "n" represents the total number of options or choices available (9 movie soundtracks), and "r" represents the number of choices that Chris wants to make (3 movie soundtracks).
Now let's substitute the values into the formula and calculate the number of different selections:
C(9, 3) = 9! / (3! * (9 - 3)!)
First, let's calculate the factorial of 9:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3* 2 * 1 = 362,880
Next, let's calculate the factorial of 3:
3! = 3 * 2 * 1 = 6
And lastly, let's calculate the factorial of (9-3):
(9 - 3)! = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Now we can substitute these values back into the formula:
C(9, 3) = 362,880 / (6 * 720)
Simplifying further:
C(9, 3) = 362,880 / 4,320
Cancelling out common factors:
C(9, 3) = 84
Therefore, there are 84 different selections of movie soundtracks that Chris can purchase from the available options.