4.E: Combinations (Optional Exercises)
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Do the following problems using combinations.
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How many different 3-people committees can be chosen from ten people?
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How many different 5-player teams can be chosen from eight players?
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In how many ways can a person chose to vote for three out of five candidates on a ballot for a school board election?
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Compute the following:
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9C2
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6C4
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8C3
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7C4
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How many 5-card hands can be chosen from a deck of cards?
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How many 13-card bridge hands can be chosen from a deck of cards?
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There are twelve people at a party. If they all shake hands, how many different hand-shakes are there?
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In how many ways can a student choose to do four questions out of five on a test?
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Five points lie on a circle. How many chords can be drawn through them?
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How many diagonals does a hexagon have?
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There are five team in a league. How many games are played if every team plays each other twice?
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A team plays 15 games a season. In how many ways can it have 8 wins and 7 losses?
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In how many different ways can a 4-child family have 2 boys and 2 girls?
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A coin is tossed five times. In how many ways can it fall three heads and two tails?
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The shopping area of a town is a square that is six blocks by six blocks. How many different routes can a taxi driver take to go from one corner of the shopping area to the opposite cater-corner?
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If the shopping area in the previous problem has a rectangular form of 5 blocks by 3 blocks, then how many different routes can a taxi driver take to drive from one end of the shopping area to the opposite kitty corner end?
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A team of 7 workers is assigned to a project. In how many ways can 3 of the 7 workers be selected to make a presentation to the management about their progress on the project?
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A real estate company has 12 houses listed for sale by their clients. In how many ways can 5 of the 12 houses be selected to be featured in an advertising brochures?
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A frozen yogurt store has 9 toppings to choose from. In how many ways can 3 of the 9 toppings be selected ?
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A kindergarten teacher has 14 books about a holiday. In how many ways can she select 4 of the books to read to her class in the week before the holiday?
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