9C0 =
9C0 = 1
To find the value of 9C0, we can use the combination formula. The combination formula is given by:
nCk = n! / (k!(n-k)!)
In this case, we need to find 9C0, which means we are choosing 0 objects from a set of 9 objects. According to the combination formula, we have:
9C0 = 9! / (0!(9-0)!)
Since we have 0! and 9-0 = 9, we can simplify this to:
9C0 = 9! / (1 * 9!)
Now, the factorial of a number is defined as the product of all positive integers less than or equal to the number. In this case:
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
Simplifying further:
9! = 362,880
Now substituting the value into the combination formula:
9C0 = 362,880 / (1 * 362,880)
We can simplify this as:
9C0 = 1
Therefore, the value of 9C0 is 1.
The expression 9C0 represents the combination of choosing 0 items out of a total of 9 items. To calculate this combination, we can use the formula for combinations:
nCr = n! / (r!(n-r)!),
where n is the total number of items and r is the number of items to be chosen.
In this case, n = 9 and r = 0, so the calculation becomes:
9C0 = 9! / (0!(9-0)!) = 9! / (0!9!) = 1.
Therefore, 9C0 equals 1.