We are told that Alejandra can invite two out of four friends to go out to dinner for her birthday. We want to find the number of the possible outcomes of this situation. Let F_1, F_2, F_3, and F_4 represent four friends of Alejandra. We will make a table to show all possible outcomes of this event. We will list the outcomes of the first choice in the left column and those of the second choice in the top row.
F_1
F_2
F_3
F_4
F_1
-
F_1,F_2
F_1,F_3
F_1,F_4
F_2
F_2,F_1
-
F_2,F_3
F_2,F_4
F_3
F_3,F_1
F_3,F_2
-
F_3,F_4
F_4
F_4,F_1
F_4,F_2
F_4,F_3
-
From the table notice that the identically colored outcomes are the same, because inviting F_1 first then inviting F_2 is the same as inviting F_2 first than inviting F_1. Therefore, we will count the same colored outcomes once.
Outcomes
F_1, F_2
F_1, F_3
F_1, F_4
F_2, F_3
F_3, F_4
There are 6 possible outcomes of inviting two out of four friends. With this information, the correct option is D.
