Four Practice Problems:
Permutations and
Combinations
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Problem 1
QUESTION: In how many ways can 3 men each be assigned to a hotel room if there are 8 hotel rooms available? (One room is as good as any other.)
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Solution 1
- We're drawing X = 3 rooms from a mother set of n = 8 rooms.
- The order of the rooms is of no concern, so it's a combination.
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Problem 2
QUESTION: Bob has prepared 7 dishes for a special dinner for his new girlfriend. She tells him that she can only eat 4 of them. So now Bob has to decide what to serve her and in what order.
In how many different ways can Bob serve a different sequence of 4 dishes from a line-up of 7 different dishes?
(Click on the down arrow for the solution.)
Solution 2
- The order in which Bob serves the dishes matters, so it's a (partial) permutation.
- n = 7 and X = 4
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Problem 3
QUESTION: Bob has 4 kids, but only 2 pieces of candy. (The candy is the same.) So he decides to just give the candy to the first 2 kids he sees when he gets home.
In how many ways can Bob give 2 of his kids candy?
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Solution 3
- Since the order that the two chosen kids gets the candy doesn't matter (e.g., Billy then Bobby = Bobby then Billy), it's a combination with n = 4 and X = 2.
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Problem 4
QUESTION: Bob has 5 employees but only 3 parking spots for them. The one next to the door is the best spot; the worst is the one by the dumpster. These 5 employees race every day to get to work first to grab these parking spots.
How many ways can the 5 employees grab those 3 parking spots?
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Solution 4
- Since it matters which parking spot you get, the order matters. This is a permutation.
- n = 5, X = 3
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1. Probability - Permutation and Combination Problems
By smilinjoe
1. Probability - Permutation and Combination Problems
Multinomial arrangements of mother sets sorted into two groups (= binomial arrangements).
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