Question

Which of these situations involves a combination?A: Determining how many different groups of 3 employees can be chosen from 10 employees.B: Determining how many different seating charts can be made seating 7 people at a table.C: Determining how many different 6 letter passwords can be made using the letters in "pencil”.D: Determining the lane assignments for 8 runners.

Answer 1

Let's remember the definition of a combination, which is a mathematical techinque that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Let's focus on the fact that order does not matter. Since this is the case, option C does not involve a combination, as the password "pencil" is different from the password "licnep", so the order matters in this case.

We can also discard option D, since it's not the same whether runner 1 is in the first lane or if they are in the third, order matters in this case.

That leaves us with options A and B. Since we are given no information about the employees or how they are being sorted into groups, we can assume the order in which they are sorted does not matter.

Likewise, since we are given no information about the people sitting at the table or the criteria used to sort them, we can assume the order is irrelevant.

In conclussion, options A and B involve a combination, while options C and D do not.