SECTION 7.4 PROBLEM SET: CIRCULAR PERMUTATIONS AND PERMUTATIONS WITH SIMILAR ELEMENTS Do the following problems using the techniques learned in this section. In how many different ways can five children 2) In how many ways can three people be made to hold hands to play "Ring Around the Rosy"? sit at a round table? 3) In how many different ways can six children 4) In how many ways can three couples be seated ride a "Merry Go Around" with six horses? at a round table, so that men and women sit alternately? 5) In how many ways can six trinkets be arranged | 6) In how many ways can five keys be put on a on a chain? key ring? 7) Find the number of different permutations of Find the number of different permutations of the letters of the word MASSACHUSETTS. the letters of the word MATHEMATICS.SECTION 7.4 PROBLEM SET: CIRCULAR PERMUTATIONS AND PERMUTATIONS WITH SIMILAR ELEMENTS 9) Seven flags are to be flown on seven poles: 10) How many different ways can 3 pennies, 2 3 flags are red, 2 are white, and 2 are blue,/ nickels and 5 dimes be arranged in a row? How many different arrangements are possible? 1 1) How many four-digit numbers can be made 12) How many five-digit numbers can be made using wo 2's and two 3's? using two 6's and three 7's? 13) If a coin is tossed 5 times, how many different |14) If a coin is tossed 10 times, how many different outcomes of 3 heads and 2 tails are possible? outcomes of 7 heads and 3 tails are possible? 15) If a yeam plays ten games, how many different 16) If a team plays ten games, how many different outcomes of 6 wins and 4 losses are possible? ways can the team have a winning season