Express (12/4) in factorial notation (i.e. using the nCr formula). Evaluate.
12C4 = 12! / 8!4! = 12*11*10*9 / 1*2*3*4
Count down r factors from n on top, count up r factors from 1 on the bottom
To express (12/4) in factorial notation using the nCr formula, we need to evaluate 12! / (4! * (12-4)!).
First, let's calculate the factorials:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
4! = 4 x 3 x 2 x 1
(12-4)! = 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Then, substitute these values into the nCr formula and simplify:
(12/4) = 12! / (4! * (12-4)!)
= (12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / (4 x 3 x 2 x 1) * (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)
= (12 x 11 x 10 x 9) / (4 x 3 x 2 x 1)
= 11880 / 24
= 495
So, (12/4) in factorial notation is 495.