Question

Fiona chooses three towels from a group of five to pack in her beach bag for herself and her two brothers. Let the five towels be represented by A,B,C,D, and E.

If Fiona chooses towel A for herself, which statements about the possible outcomes for her brothers’ towels are true? Select three options.

There are 10 possible ways to choose the group of towels.
The combination BC is not the same as CB.
She has four choices for the first brother’s towel and three choices for the second brother’s towel.
ABC, ABD, ABE, ACD, ACE, and ADE are the possible outcomes.
If Fiona did not choose towel A for herself, there would be more outcomes.

Answer 1

Correct choices: 1, 3, and 4.

Brief reasons:
- (1) True: overall there are C(5,3) = 10 ways to choose 3 towels from 5.
- (3) True: with A fixed, for ordered assignments the first brother has 4 choices and then the second has 3.
- (4) True: with A fixed, the unordered groups including A are ABC, ABD, ABE, ACD, ACE, ADE (6 total).

(2) is false because as a combination BC = CB. (5) is false because whether Fiona picks A or any other towel, the number of possible pairs for the brothers is the same (C(4,2)=6).