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.(b) Determine the number of different arrangements 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 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 only the items in the group is of concern.

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.

Suppose we want to choose 6 letters, without replacement, from 12 distinct letters.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices is taken into consideration?(b) How many ways can this be done, if the order of the choices is not taken into consideration?

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.

From 12 students, in how many ways you can select four members of the committee?Group of answer choices480485490495