Andwer: 8C6= 28
The formula for a combination of choosing r unique ways from n possibilities is:
nCr = n! r!(n - r)!
where n is the number of items and r is the unique arrangements.
Plugging in our numbers of n = 8 and r = 6, we get:
8C6 = 8!
6!(8 - 6)!
Calculate the numerator n!:
n! = 8!
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
8! = 40,320
Calculate the first denominator (n - r)!:
(n - r)! = (8 - 6)!
(8 - 6)! = 2!
2! = 2 x 1
2! = 2
Calculate the second denominator r!:
r! = 6!
6! = 6 x 5 x 4 x 3 x 2 x 1
6! = 720
Calculate our combination value nCr for n = 8 and r = 6:
8C6 = 40,320
720 x 2
8C6 = 40,320
1,440
8C6 = 28
