In how many ways can two pool balls be chosen out of sixteen?

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