BMS Mathematics Academic Team Practice Test 2026 - Free Math Practice Questions and Study Guide

To determine the number of ways to choose two pool balls from a total of sixteen, we can use the concept of combinations, which is used when the order of selection does not matter. The formula for combinations is given by:

\[

\binom{n}{r} = \frac{n!}{r!(n - r)!}

\]

Where:

- \( n \) is the total number of items to choose from (in this case, 16 pool balls),

- \( r \) is the number of items to choose (in this case, 2).

Substituting the values into the formula, we have:

\[

\binom{16}{2} = \frac{16!}{2!(16 - 2)!} = \frac{16!}{2! \cdot 14!}

\]

Here, the \( 16! \) in the numerator and the \( 14! \) in the denominator cancel each other out:

\[

\frac{16 \times 15}{2!} = \frac{16 \times 15}{2 \times 1} = \frac{240}{2} = 120

\]

Thus, the total number of