How do you evaluate {}^9{C_3}?

To evaluate {}^9{C_3}, you need to calculate the number of combinations of 9 items taken 3 at a time. The formula for combinations is given by:

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

where n is the total number of items, r is the number of items taken at a time, and "!" denotes the factorial of a number.

In this case, {}^9{C_3} can be calculated as follows:

{}^9{C_3} = 9! / (3! * (9 - 3)!)

Now, let's calculate step-by-step:

Calculate the factorial of 9: 9! = 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 362,880.
Calculate the factorial of 3: 3! = 3 × 2 × 1 = 6.
Calculate the factorial of (9 - 3) which is 6: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720.
Now, plug these values into the formula:

{}^9{C_3} = 362,880 / (6 * 720) ≈ 84.

Therefore, the value of {}^9{C_3} is approximately 84.