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 combinations rule, since only the items in the group is of concern. Use the combinations rule, since the number of arrangements within each group is of interest.    Use the permutations 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.

(b) Determine the number of different arrangements of 5 items that can be selected from 12 distinct items.

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.    Use the combinations rule, since only the items in the group is of concern. Use the permutations rule, since the number of arrangements within each group is of interest.

Answer 1

When the order does matter it is a Permutation.

When the order doesn't matter, it is a Combination.

a. Use the combinations rule, since only the items in the group is of concern.

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