Evaluate
12C8
The expression 12C8 represents the number of ways to choose 8 items from a set of 12 distinct items.
Using the formula for combinations:
12C8 = 12! / (8! * (12-8)!)
12C8 = 12! / (8! * 4!)
12C8 = (12*11*10*9)/(4*3*2*1)
12C8 = 495
Therefore, there are 495 ways to choose 8 items from a set of 12 distinct items.
To evaluate 12C8, you can use the formula for combinations:
nCr = n! / [(n-r)! * r!]
In this case, n = 12 and r = 8.
12! / [(12-8)! * 8!]
= 12! / [4! * 8!]
Let's calculate the factorials:
12! = 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Plugging these values into the formula:
12! / [4! * 8!]
= (12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / [(4 * 3 * 2 * 1) * (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)]
Now we can simplify the expression:
Cancel out the common factors:
= (12 * 11 * 10 * 9) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
Multiply the remaining factors:
= 19,110 / 40,320
Simplifying the fraction, we get:
= 0.4747475
Therefore, 12C8 is approximately equal to 0.4747475.