Sure! Let's carefully consider each statement and determine whether it fits the description of permutations.
1. Any arrangement of r objects selected from a single group of n possible objects
A permutation involves selecting and arranging a certain number of objects (r) from a larger set (n) of objects. The concept emphasizes choosing r objects from n and then arranging them. This statement accurately describes permutations.
2. The order is not important
In permutations, the order in which the objects are arranged matters. If the order were not important, we would be talking about combinations instead of permutations. This statement does not describe permutations.
3. Total number of arrangements is equal to m x n
This statement is not related to permutations. The number of arrangements in permutations is calculated using a factorial formula, not by simply multiplying two numbers (m and n). Therefore, this statement does not describe permutations.
4. The order is important
This statement correctly reflects a fundamental aspect of permutations. The arrangement's order is crucial when working with permutations.
Thus, the statements that best describe permutations are:
- Any arrangement of r objects selected from a single group of n possible objects
- The order is important
