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Discrete Math: Combinatorics
Combinatorics can often be thought of as counting without actually counting.
Many combinatorics problems have so many solutions that it would be hard
to systematically count them or list them all. Instead formulas, such as the
formulas for permutations, can be used to quickly "count" the number of
solutions to a problem without physically counting them.
For background information elsewhere on our site, explore the High School
Discrete Math and
Permutations and
Combinations areas of the Ask Dr. Math archives. To find relevant
sites on the Web, browse and search
Discrete Mathematics
in our Internet Mathematics Library.
Access to these problems requires a Membership.
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The Bracelet Craze
- Leigh Nataro
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Discrete Math, difficulty level 3. Find how many ways beads can be arranged around a bracelet.
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Deranged Uncle Al
- Ethel Breuche
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Discrete Math, difficulty level 3. Deranged Uncle Al allows each of his four nephews to select a toy, and buys them the four toys. How many different ways can he give each of the boys a toy so that no boy receives the toy he actually selected?
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The Doughnut Dilemma
- Leigh Nataro
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Discrete Math, difficulty level 3. How many ways can you choose three doughnuts from six different types of doughnuts?
... more>>
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A Great Way to Make Money?
- Leigh Nataro
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Discrete Math, difficulty level 2. Is it better to rely on a weekly pay of $10, or take a chance on the money that is in a paper bag?
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Happy Birthday to You, & You, & You...
- Leigh Nataro
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Trig/Calc, difficulty level 3. What is the probability that in a room of 30 people, at least two people will share the same birthday?
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Paper, Scissors, Rock
- Leigh Nataro
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Discrete Math, difficulty level 2. How many ways can Timmy go broke or win $3 in the game of paper, scissors, rock?
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Ping Pong Tournament
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Discrete Math, difficulty level 3. Organize a Ping Pong (table tennis) singles tournament for your class.
... more>>
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Seating Arrangements
- Leigh Nataro
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Discrete Math, difficulty level 3. How many different ways can three people sit at a 10-seat counter so that there are empty seats between them?
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Timeline Trivia
- Leigh Nataro
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Discrete Math, difficulty level 5. What is the probability of getting all ten historical events in the wrong order?
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Ursala is Undecided
- Melissa Kennedy, Ethel Breuche
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Discrete Math, difficulty level 1. Poor Undecided Ursala has many paths to choose to get from point A to point S. Exactly how many paths does she have a choice of taking?
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Vinnie Valentine's Mix-Up
- Leigh Nataro
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Trig/Calc, difficulty level 4. What is the probability of getting exactly 10 out of 20 valentines to the correct person?
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Welcome Back
- Leigh Nataro
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Discrete Math, difficulty level 3. Find the probability of spelling "Welcome Back" when cards with each letter are flipped over.
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World Series Champions
- Leigh Nataro
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Trig/Calc, difficulty level 3. How many ways could a baseball team win a World Series of n games if it must win a majority (one more than half) of the games played?
... more>>
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Your Phone Number, Please
- Ethel Breuche
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Discrete Math, difficulty level 1. What is the least number of area codes necessary to guarantee that the thirty million phones needed in a state have distinct ten-digit telephone numbers?
... more>>
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