Evaluate C(13, 6).
C(13, 6)
= 13!/(6!7!)
= 1716
13!/(7! 6!) =
13*12*11*10*9*8/(6*5*4*3*2) =
13*11*(12/6)*(10/5)*(9/3)*(8/(4*2)) =
13*11*2*2*3 =
(12^2 - 1)*2*2*3=
143*2*2*3=
429*4=
(430-1)*4=
1716
most calculators have that function build in.
look for a key that looks something like
nCr
To evaluate C(13, 6), we need to use the formula for the combination:
C(n, k) = n! / (k! * (n-k)!)
In this case, we have n = 13 and k = 6.
First, let's calculate the factorials involved:
n! = 13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800
k! = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
(n-k)! = (13-6)! = 7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Now, we can substitute these values into the combination formula:
C(13, 6) = 13! / (6! * (13-6)!)
= 3,628,800 / (720 * 5,040)
= 3,628,800 / 3,628,800
= 1
Therefore, C(13, 6) = 1.