You have a carrying case that holds four CDs. You want to know in how many ways you can place four of the ten CDs you own into the case.
what is C(10,4)
or 10!/(4!6!) ?
To solve this problem, we can use the concept of combinations.
The formula for calculating the number of combinations is given by:
nCr = n! / (r!(n-r)!)
Where n is the total number of items and r is the number of items to be chosen.
In this case, we want to find the number of ways to choose 4 CDs out of a total of 10 CDs.
Applying the formula, we get:
10C4 = 10! / (4!(10-4)!) = 10! / (4!6!)
Now, let's calculate the factorial values:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800
4! = 4 x 3 x 2 x 1 = 24
6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
Substituting these values into the formula, we have:
10C4 = 3,628,800 / (24 x 720) = 210
So, there are 210 different ways to place four out of the ten CDs you own into the carrying case.