1. The problem asks to calculate the binomial coefficient $\binom{9}{2}$, which means "9 choose 2". 2. The binomial coefficient formula is given by: $$\binom{n}{k} = \frac{n!}{k! (n-k)!}$$ where $n!$ denotes factorial of $n$. 3. Substitute $n=9$ and $k=2$: $$\binom{9}{2} = \frac{9!}{2! (9-2)!} = \frac{9!}{2! 7!}$$ 4. Simplify the factorial expression: $$9! = 9 \times 8 \times 7!$$ So, $$\binom{9}{2} = \frac{9 \times 8 \times 7!}{2! \times 7!} = \frac{9 \times 8}{2!}$$ 5. Calculate $2! = 2 \times 1 = 2$: $$\binom{9}{2} = \frac{9 \times 8}{2}$$ 6. Perform the multiplication and division: $$\frac{72}{2} = 36$$ 7. Therefore, the number of ways to choose 2 objects from 9 is: $$\boxed{36}$$