Final answer:
To evaluate the expression 4C2 * 6C1 / 18C3, calculate each combination separately and substitute the values into the expression.
Step-by-step explanation:
To evaluate the expression 4C2 * 6C1 / 18C3, we need to calculate each combination. C(n,r) represents the number of ways to choose r items from a set of n items.
Step 1: Calculate each combination:
4C2 = 4! / (2! * (4-2)!) = 4 * 3 / (2 * 1) = 6
6C1 = 6! / (1! * (6-1)!) = 6! / 5! = 6
18C3 = 18! / (3! * (18-3)!) = 18 * 17 * 16 / (3 * 2 * 1) = 816
Step 2: Substitute the values into the expression:
4C2 * 6C1 / 18C3 = 6 * 6 / 816 = 1/68
Therefore, the value of the expression is 1/68.