1. The problem is to determine the value of $16C2$, which represents the number of combinations of 16 items taken 2 at a time. 2. The formula for combinations is: $$nCr = \frac{n!}{r!(n-r)!}$$ where $n$ is the total number of items, and $r$ is the number of items chosen. 3. Substitute $n=16$ and $r=2$ into the formula: $$16C2 = \frac{16!}{2!(16-2)!} = \frac{16!}{2!14!}$$ 4. Simplify the factorial expression by canceling $14!$ from numerator and denominator: $$16C2 = \frac{16 \times 15 \times \cancel{14!}}{2! \times \cancel{14!}} = \frac{16 \times 15}{2!}$$ 5. Calculate $2! = 2 \times 1 = 2$: $$16C2 = \frac{16 \times 15}{2}$$ 6. Perform the multiplication and division: $$16C2 = \frac{240}{2} = 120$$ 7. Therefore, the number of combinations of 16 items taken 2 at a time is $120$.