assignment for an art class is to complete 4 projects from a list of 6. how many ways can this be done if the order soes not matter?
you are "choosing" 4 form 6
C(6,4) = 6!/(4!2!) = 15
To find the number of ways to complete 4 projects from a list of 6 where the order does not matter, you can use the combination formula.
The formula to find the number of combinations of selecting r items from a set of n items is given by:
C(n, r) = n! / (r! * (n-r)!)
In this case, n = 6 (the total number of projects) and r = 4 (the number of projects to be completed).
Plugging these values into the formula:
C(6, 4) = 6! / (4! * (6-4)!)
Simplifying the equation:
C(6, 4) = 6! / (4! * 2!)
You can calculate the factorial values as follows:
6! = 6*5*4*3*2*1 = 720
4! = 4*3*2*1 = 24
2! = 2*1 = 2
Therefore,
C(6, 4) = 720 / (24 * 2) = 15
So, there are 15 different ways to complete the 4 projects from the list of 6, where the order does not matter.