7.4.1: Circular Permutations and Permutations with Similar Elements (Exercises)
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Do the following problems using the techniques learned in this section.
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In how many different ways can five children hold hands to play "Ring Around the Rosy"?
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In how many ways can three people be made to sit at a round table?
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In how many different ways can six children ride a "Merry Go Around" with six horses?
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In how many ways can three couples be seated at a round table, so that men and women sit alternately?
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In how many ways can six trinkets be arranged on a chain?
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In how many ways can five keys be put on a key ring?
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Find the number of different permutations of the letters of the word MASSACHUSETTS.
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Find the number of different permutations of the letters of the word MATHEMATICS.
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Seven flags are to be flown on seven poles: 3 flags are red, 2 are white, and 2 are blue,. How many different arrangements are possible?
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How many different ways can 3 pennies, 2 nickels and 5 dimes be arranged in a row?
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How many four-digit numbers can be made using two 2's and two 3's?
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How many five-digit numbers can be made using two 6's and three 7's?
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If a coin is tossed 5 times, how many different outcomes of 3 heads and 2 tails are possible?
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If a coin is tossed 10 times, how many different outcomes of 7 heads and 3 tails are possible?
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If a team plays ten games, how many different outcomes of 6 wins and 4 losses are possible?
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If a team plays ten games, how many different ways can the team have a winning season?
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