THE NUMBER OF COMBINATIONS OF n OBJECTS TAKEN m AT A TIME IS DENOTED BY Select one: P_(n) A_(m)^n O A_(n)^m P_(k) C_(n)

The correct answer is $C_{n}^{m}$.<br /><br />The number of combinations of n objects taken m at a time is denoted by $C_{n}^{m}$, which is also written as $\binom{n}{m}$ or "n choose m". It represents the number of ways to choose m objects from a set of n objects without considering the order of selection.<br /><br />The formula for calculating the number of combinations is:<br /><br />$C_{n}^{m} = \frac{n!}{m!(n-m)!}$<br /><br />where n! (n factorial) is the product of all positive integers from 1 to n, m! is the product of all positive integers from 1 to m, and (n-m)! is the product of all positive integers from 1 to (n-m).<br /><br />The other options provided are not correct for this context:<br /><br />- $P_{n}$ is not a standard notation for combinations.<br />- $A_{m}^{n}$ and $A_{n}^{m}$ are not standard notations for combinations.<br />- $P_{k}$ is not a standard notation for combinations.<br />- $C_{n}$ is not a standard notation for combinations.