Evaluate the quantity
5* P(6,2) * C(10,5)
just apply the definitions of P and C
5 * (6*5) * (10*9*8*7*6)/(1*2*3*4*5)
I doubt that.
shut up damon i looked it up and its correct you h03
To evaluate the quantity 5 * P(6,2) * C(10,5), we need to understand what P(6,2) and C(10,5) represent.
P(6,2) stands for the permutation of 6 objects taken 2 at a time. In other words, it represents the number of ways we can arrange 2 objects from a set of 6 objects without repetition and where the order matters.
C(10,5) stands for the combination of 10 objects taken 5 at a time. In other words, it represents the number of ways we can choose 5 objects from a set of 10 objects without repetition and where the order doesn't matter.
Let's evaluate each term separately:
P(6,2) = 6! / (6-2)! = 6! / 4! = (6 * 5 * 4!) / 4! = 6 * 5 = 30
C(10,5) = 10! / (5! * (10-5)!) = 10! / (5! * 5!) = (10 * 9 * 8 * 7 * 6!) / (5 * 4 * 3 * 2 * 1 * 5!) = (10 * 9 * 8 * 7) / (5 * 4 * 3 * 2) = 252
Now, substitute these values back into the original expression:
5 * P(6,2) * C(10,5) = 5 * 30 * 252 = 15,000
Therefore, the value of the given quantity is 15,000.