For each of the following decide whether you would compute the number of possibl

Question

For each of the following decide whether you would compute the number of possible outcomes with a permutation (order matters and without replacement), a combination (order doesn’t matter and without replacement), or neither (with replacement). Note you do not need to compute anything. However, you must provide a brief explanation of why you chose your answer.

(a) The university president named 3 new officers: a vice-president of finance, a vice president of academics, and a vice-president of students.

(b) The university president selected two vice-presidents to attend graduation.

(c) A student checked out four novels from the library at the same time.

(d) A father ordered an ice cream cone for each of his four children. He could choose the flavors among: chocolate, vanilla, and strawberry

Explanation / Answer

a) Permutation: because once the officer is selected for any of the post, we cannot replacethem, ie. only one officer must be selected for one position, and here order also matters, because President has to appoint officers in different departments.

b) Combination: he has to select randomly 2 vice presidents from a group of vice presidents. For selectioon of any 2 VPs, order doesnot matters and once he select one VP, he cannot replace them.

c) Combination : because student selects randomly 4 novels and order doesnot matter and that too without replacement,

d) Neither : because father order icecream according to the choice of his children, and all 4 or less can have same or different flavors of icecream.

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