Explanation:

To solve this problem, we need to use the formula for the combination (nCr), which is given by:

nCr = n! / (r!(n-r)!)

where n is the total number of objects, and r is the number of objects chosen at a time.

Given that nC8 = nC2, we can set up the equation as follows:

n! / (8!(n-8)!) = n! / (2!(n-2)!)

To simplify the equation, we can cancel out the common terms on both sides:

(n-2)! * 8! = (n-8)! * 2!

Now, let's expand the factorials:

(n-2)! * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = (n-8)! * 2 * 1

Cancel out the common terms:

8 * 7 * 6 * 5 * 4 * 3 = (n-8)!

We are left with:

8 * 7 * 6 * 5 * 4 * 3 = (n-8)!

Now, let's evaluate the factorial on the left side:

8 * 7 * 6 * 5 * 4 * 3 = 20160

So, we have:

20160 = (n-8)!

To find the value of n, we need to determine the value of (n-8)!. We can do this by finding the factorial of numbers from 1 to 8 until we find a number that is equal to or greater than 20160.

By evaluating the factorials, we find that 8! = 40320, which is greater than 20160. The next factorial, 7!, is equal to 5040, which is less than 20160.

Therefore, n must be greater than 8 but less than 16. The only option that satisfies this condition is option 'C', which is 10.

Hence, the correct answer is option 'C'.