What is the main difference between a situation in which the use of the permutations rule is appropriate and one in which the use of the combinations rule is appropriate?Permutations count the number of different arrangements of r out of n items, while combinations count the number of groups of r out of n items.Both permutations and combinations count the number of groups of r out of n items.    Combinations count the number of different arrangements of r out of n items, while permutations count the number of groups of r out of n items.Both permutations and combinations count the number of different arrangements of r out of n items.

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

basic concepts of permutations and combinations

A combination lock uses three numbers between 1 and 79 with repetition, and they must be selected in the correct sequence.Which of the five counting rules is used to find that number?factorial ruleFundamental counting rule    Combinations rulePermutations rule (when all of the items are different)Permutations rule (when some items are identical to others)How many different "combinations" are possible? Is the name of "combination lock" appropriate? If not, what other name would be better?No. The name "permutation lock" is more appropriate.No. The name "factorial lock" is more appropriate.      No the name "number lock" is more appropriate because "fundamental counting rule lock" is awkward.Yes. The name "combination lock" is appropriate.

How many different "combinations" are possible? Is the name of "combination lock" appropriate? If not, what other name would be better?No. The name "permutation lock" is more appropriate.No. The name "factorial lock" is more appropriate.      No the name "number lock" is more appropriate because "fundamental counting rule lock" is awkward.Yes. The name "combination lock" is appropriate.

Which of the following types of permutation can be used when you want to know how many arrangements of letters can you make from the word MATHEMATICS?Group of answer choicesDistinct with RepetitionDistinct without RepetitionNondistinct PermutationCircular Permutation