simplify 8C5
The "C" stands for combinations ( like combinations and permutations )
8C5 =
8*7*6*5*4
-------------
1*2*3*4*5
Note that this es equal to
8C3 = (8*7*6)/(1*2*3)
because the 4*5 just cancels out.
to figure nCm, just start with n, and count down for m factors in the top, and starting with 1, count up for m factors in the bottom.
If m > n/2, you can use n-m instead of m, as shown above.
To simplify 8C5, you need to use the formula for combinations, which is:
nCr = n! / (r!(n-r)!),
where:
n = the total number of items
r = the number of items to be chosen
Applying this formula to your problem, we have:
8C5 = 8! / (5!(8-5)!)
Now, let's simplify the expression step by step:
First, calculate the factorials:
8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
5! = 5 x 4 x 3 x 2 x 1
(8-5)! = 3! = 3 x 2 x 1
Next, substitute these values into the formula:
8C5 = 8! / (5!(8-5)!)
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / ((5 x 4 x 3 x 2 x 1)(3 x 2 x 1))
Simplify the expression further:
8C5 = (8 x 7 x 6) / (3 x 2 x 1)
= (336) / (6)
= 56
Therefore, 8C5 simplifies to 56.