fiona chooses three towels from a group of five to pack in her beach bag for herself and her two brothers…

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.\nif fiona chooses towel a for herself, which statements about the possible outcomes for her brothers towels are true? select three options.\nthere are 10 possible ways to choose the group of towels.\nthe combination bc is not the same as cb.\nshe has four choices for the first brothers towel and three choices for the second brothers towel.\nabc, abd, abe, acd, ace, and ade are the possible outcomes.\nif fiona did not choose towel a for herself, there would be more outcomes.

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.\nif fiona chooses towel a for herself, which statements about the possible outcomes for her brothers towels are true? select three options.\nthere are 10 possible ways to choose the group of towels.\nthe combination bc is not the same as cb.\nshe has four choices for the first brothers towel and three choices for the second brothers towel.\nabc, abd, abe, acd, ace, and ade are the possible outcomes.\nif fiona did not choose towel a for herself, there would be more outcomes.

Answer

Explanation:

Step1: Analyze the number of ways

Since Fiona has already chosen towel A for herself, we need to choose 2 towels out of the remaining 4 (B, C, D, E) for her brothers. The number of ways to choose 2 towels out of 4 is given by the combination formula (C(n,r)=\frac{n!}{r!(n - r)!}), where (n = 4) and (r=2). So (C(4,2)=\frac{4!}{2!(4 - 2)!}=\frac{4\times3\times2!}{2!\times2!}=\frac{4\times3}{2\times 1}=6), not 10. So the first option is wrong.

Step2: Check combination property

Combinations are not order - sensitive. The combination of choosing B and C is the same as choosing C and B. So the second option is wrong.

Step3: Analyze the choice for brothers

After choosing A for herself, for the first brother, she has 4 choices (B, C, D, E). After choosing a towel for the first brother, for the second brother, she has 3 choices. So the third option is correct.

Step4: List possible outcomes

The possible groups (since A is already chosen) are ABC, ABD, ABE, ACD, ACE, ADE. So the fourth option is correct.

Step5: Analyze the case when A is not chosen

If A is not chosen, we need to choose 3 towels out of 5. The number of ways is (C(5,3)=\frac{5!}{3!(5 - 3)!}=\frac{5\times4\times3!}{3!\times2!}=10). When A is chosen, we have 6 ways. So if Fiona did not choose towel A for herself, there would be more outcomes. So the fifth option is correct.

Answer:

C. She has four choices for the first brother’s towel and three choices for the second brother’s towel, D. ABC, ABD, ABE, ACD, ACE, and ADE are the possible outcomes, E. If Fiona did not choose towel A for herself, there would be more outcomes.