Question

For each of the following situations, explain why the combinations rule or the permutations rule should be used. (a) Determine the number of different groups of 5 items that can be selected from 12 distinct items. Use the permutations rule, since the number of arrangements within each group is of interest. Use the combinations rule, since the number of arrangements within each group is of interest. Use the permutations rule, since only the items in the group is of concern.

Answer 1

Use the combinations rule, since the number of arrangements within each group is of interest.

Explanation:

Arrangments rule:

Number of items to be arranged is the same as the number of places.

Permutations formula:

Number of items to be arranged is different of the number of places, and the order in which the items are placed is important(AB and BA are different outcomes).

Combinations formula:

Number of items to be arranged is different of the number of places, and the order in which the items are placed is not important(AB and BA are the same outcomes).

In this question:

5 items from a set of 12. The order in which the items are chosen is not important(for example, a book and a pencil would be the same as a pencil and a book). So the combinations formula is used, and the correct option is given by:

Use the combinations rule, since the number of arrangements within each group is of interest.