finding possible outcomes\neli chooses two shirts from a group of five to pack for a weekend trip. let each…

finding possible outcomes\neli chooses two shirts from a group of five to pack for a weekend trip. let each shirt be represented by a, b, c, d, and e. which statements about the situation are true? check all that apply.\nthe combination of ab and ba are the same.\neach shirt can be paired with any one of other the remaining shirts.\nthere are twenty possible ways to choose the group of shirts.\nhe has five choices for the first shirt and five choices for the second shirt.\nif he chooses shirt b, there are four possible outcomes for choosing the second shirt.

finding possible outcomes\neli chooses two shirts from a group of five to pack for a weekend trip. let each shirt be represented by a, b, c, d, and e. which statements about the situation are true? check all that apply.\nthe combination of ab and ba are the same.\neach shirt can be paired with any one of other the remaining shirts.\nthere are twenty possible ways to choose the group of shirts.\nhe has five choices for the first shirt and five choices for the second shirt.\nif he chooses shirt b, there are four possible outcomes for choosing the second shirt.

Answer

Explanation:

Step1: Understand combination concept

In combinations, order doesn't matter. So AB and BA are the same.

Step2: Analyze shirt - pairing

Each shirt can be paired with any of the remaining 4 shirts.

Step3: Calculate number of combinations

The number of ways to choose 2 shirts out of 5 is given by the combination formula $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 5$ and $k=2$. $C(5,2)=\frac{5!}{2!(5 - 2)!}=\frac{5\times4}{2\times 1}=10$, not 20 or 5.

Step4: Consider shirt - choosing steps

For the first shirt, there are 5 choices. For the second shirt, there are 4 remaining choices.

Step5: Analyze a single - shirt case

If he chooses shirt B first, there are 4 remaining shirts to choose from for the second shirt.

Answer:

  • The combination of AB and BA are the same.
  • Each shirt can be paired with any one of other the remaining shirts.
  • If he chooses shirt B, there are four possible outcomes for choosing the second shirt.