How do you evaluate ⁸C₂?

To evaluate the expression ⁸C₂, which represents a combination, you can use the formula for combinations:

Combination Formula

The formula for combinations is:

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

In this case, n is 8 and r is 2.

Step-by-Step Calculation

• Calculate 8!: This is the factorial of 8, which is 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320.
• Calculate 2!: This is the factorial of 2, which is 2 × 1 = 2.
• Calculate (8 - 2)!: This is 6!, which equals 720.

Putting It All Together

Now, substitute these values into the combination formula:

C(8, 2) = 8! / (2! * 6!) = 40320 / (2 * 720)

Calculating the denominator:

2 * 720 = 1440

Now divide:

C(8, 2) = 40320 / 1440 = 28

Final Result

Thus, the value of ⁸C₂ is 28.