How do you evaluate ^8C_3 ?

To evaluate the combination \[^8C_3\], which is read as "8 choose 3," you use the combination formula:

\[
^nC_r = \frac{n!}{r!(n-r)!}
\]

Where:
- \(n\) is the total number of items (in this case, 8),
- \(r\) is the number of items chosen (in this case, 3),
- \(n!\) (n factorial) is the product of all positive integers up to \(n\),
- \(r!\) (r factorial) is the product of all positive integers up to \(r\).

For \[^8C_3\]:

\[
^8C_3 = \frac{8!}{3!(8-3)!} = \frac{8!}{3!5!}
\]

Now, calculate each factorial:

- \(8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40320\),
- \(3! = 3 \times 2 \times 1 = 6\),
- \(5! = 5 \times 4 \times 3 \times 2 \times 1 = 120\).

Now, substitute these values into the formula:

\[
^8C_3 = \frac{40320}{6 \times 120} = \frac{40320}{720} = 56
\]

Thus, \[^8C_3 = 56\].

So, the value of \[^8C_3\] is 56.