Compute
9(sub)C(sub)6
also written as
C(9,6)
= 9!/(6!3!) = 362880/(720*6) = 84
To compute 9C6 (read as "9 choose 6"), which represents the number of combinations of 9 items taken 6 at a time, you can use the binomial coefficient formula:
nCr = n! / (r! * (n-r)!)
In this formula, "n" represents the total number of items, and "r" represents the number of items to be chosen.
Let's calculate 9C6 using the formula:
Step 1: Calculate the factorial of 9:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
Step 2: Calculate the factorial of 6:
6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
Step 3: Calculate the factorial of (9-6):
3! = 3 * 2 * 1 = 6
Now, substitute these values into the formula:
9C6 = 9! / (6! * (9-6)!)
= 362,880 / (720 * 6)
= 362,880 / 4,320
= 84
Therefore, 9C6 equals 84.