Final answer:
To evaluate C(9,3), we can use the formula for combinations and calculate the factorials. The correct answer is B. 84.
Step-by-step explanation:
The expression C(9,3) represents the number of combinations that can be formed by choosing 3 items out of 9 without considering the order. To evaluate this expression, we can use the formula for combinations:
C(n, r) = n! / (r!(n-r)!),
where n is the total number of items and r is the number of items being chosen. Plugging in n=9 and r=3, we get:
C(9,3) = 9! / (3!(9-3)!) = 9! / (3!6!).
To simplify the expression, we can calculate the factorials:
9! = 9x8x7x6x5x4x3x2x1 = 362,880,
3! = 3x2x1 = 6, and
6! = 6x5x4x3x2x1 = 720.
Substituting these values back into the formula, we have:
C(9,3) = 362,880 / (6x720) = 84.
Therefore, the correct answer is B. 84.