QuestionIn the exercises below, does the problem involve permutations or combinations?
Select an answer Of the 100 people in the U.S. Senate, 18 serve on the Foreign Relations Committee. How many ways are there to select the members of this committee? Select an answer Nine bands have volunteered to perform at a benefit concert, but there is only enough
time for five of the bands to play. How many line ups are possible? time for five of the bands to play. How many line ups are possible?
Select an answer create?
Using 15 flavors of ice cream, how many cones with three different flavors can you
Studdy Solution
STEP 1
1. The problems involve determining whether a situation is a permutation or a combination.
2. Permutations are used when order matters.
3. Combinations are used when order does not matter.
STEP 2
1. Analyze the first problem.
2. Analyze the second problem.
3. Analyze the third problem.
STEP 3
Analyze the first problem:
- The problem involves selecting members for a committee from a group of 100 people.
- The order in which the members are selected does not matter, only the group composition matters.
Conclusion: This is a combination problem.
STEP 4
Analyze the second problem:
- The problem involves creating lineups for bands to perform.
- The order in which the bands perform matters.
Conclusion: This is a permutation problem.
STEP 5
Analyze the third problem:
- The problem involves selecting three different flavors of ice cream for a cone.
- The order in which the flavors are chosen does not matter, only the combination of flavors matters.
Conclusion: This is a combination problem.
Summary of Answers:
1. First problem: Combination
2. Second problem: Permutation
3. Third problem: Combination
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