\binom{n}{r} = \frac{n!}{r!(n-r)!}
Given:
\binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10!}{3! \cdot 7!}
Simplify the factorials:
\frac{10!}{3! \cdot 7!} = \frac{10 \cdot 9 \cdot 8 \cdot 7!}{3! \cdot 7!}
Cancel \(7!\):
\frac{10 \cdot 9 \cdot 8}{3!} = \frac{10 \cdot 9 \cdot 8}{3 \cdot 2 \cdot 1}
Calculate the numerator and denominator:
\frac{720}{6} = 120
So, the number of ways to choose 3 representatives from 10 employees is:
\boxed{120}