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. 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 brothers towel and three choices for the second brothers 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.

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 brothers towel and three choices for the second brothers 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

Explanation:

Step1: Calculate number of ways to choose 2 towels out of 4

Since Fiona has chosen towel A for herself, we need to choose 2 towels out of the remaining 4 for her brothers. The number of combinations of choosing $r$ items from $n$ items is given by the formula $C(n,r)=\frac{n!}{r!(n - r)!}$. Here $n = 4$ and $r=2$, so $C(4,2)=\frac{4!}{2!(4 - 2)!}=\frac{4!}{2!2!}=\frac{4\times3\times2!}{2!×2!}=\frac{4\times3}{2\times 1}=6$.

Step2: Analyze combination properties

In combinations, the order does not matter. So combination BC is the same as CB.

Step3: Analyze choice - making process

If Fiona has chosen towel A for herself, for the first brother's towel, she has 4 choices (B, C, D, E). After choosing a towel for the first brother, she has 3 choices left for the second brother's towel.

Step4: List possible outcomes

The possible combinations of 2 - towel groups from B, C, D, E are BC, BD, BE, CD, CE, DE. When considering the full - set with Fiona's towel A, the possible outcomes are ABC, ABD, ABE, ACD, ACE, ADE.

Step5: Consider the case if Fiona doesn't choose A

If Fiona did not choose towel A for herself, she would be choosing 1 towel out of 5 for herself first, and then 2 towels out of the remaining 4 for her brothers. The total number of ways to choose 3 towels out of 5 is $C(5,3)=\frac{5!}{3!(5 - 3)!}=\frac{5\times4\times3!}{3!×2!}=10$. So if she didn't fix towel A for herself, there would be more outcomes.

Answer:

  • 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.