Question 1104312: Use the formula nCr for to evaluate the expression.
9C1
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
The n C r formula is
n C r = (n!)/(r!(n-r)!)
The exclaimation marks mean factorial. Writing something like 6! means we start at 6 and count our way down to 1. Throughout the countdown, we multiply out the terms
6! = 6*5*4*3*2*1
So we'll be using
9! = 9*8*7*6*5*4*3*2*1
8! = 8*7*6*5*4*3*2*1
and
1! = 1
Meaning that
n C r = (n!)/(r!(n-r)!)
9 C 1 = (9!)/(1!*(9-1)!)
9 C 1 = (9!)/(1!*8!)
9 C 1 = (9*8*7*6*5*4*3*2*1)/((1)*(8*7*6*5*4*3*2*1))
9 C 1 = (362880)/((1)*(40320))
9 C 1 = (362880)/(40320)
9 C 1 = 9
As a shortcut,
n C r = (n!)/(r!(n-r)!)
9 C 1 = (9!)/(1!*(9-1)!)
9 C 1 = (9!)/(1!*8!)
9 C 1 = (9*8!)/(1!*8!)
9 C 1 = 9/1
9 C 1 = 9
which works because the 8! is buried inside of 9!, allowing us to say 9! = 9*8!
So the "8!" terms cancel out
Answer: 9
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