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1) (5pts) Three married couples have purchased theater tickets and are seated in a row consisting...
Please answer 1 and 2 show all work!!!! 1) (6pts) Three married couples have purchased theater...
Please answer 1 and 2 show all work!!!!
1) (6pts) Three married couples have purchased theater tickets and are seated in a row consisting of just six seats. a) How many different seating arrangements are possible? TOTAL: How many different seating arrangéments have the three men (in order) in the three leftmost seats? any b) TOTAL c) Assume the theater-goers take their seats in a completely random fashion. Then each of the seating arrangements in part a) are equally likely....
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events A, [ith couple sit next to each other),-1, 2, 3. Count carefully the numbers of arrangements in...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that so...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events Ai = (ith couple sit next to each other2, 3. Count carefully the numbers of arrangements in...
Four married couples have bought 8 seats in the same row for a concert. In how...
Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives?
8. Four married couples have bought 8 seats in the same row for a concert. In...
8. Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives?
Three married couples arrange themselves randomly in six consecutive seats in a row. Determine (a) the...
Three married couples arrange themselves randomly in six consecutive seats in a row. Determine (a) the number of ways the following event can occur, and (b) the probability of the event. (The denominator of the probability fraction will be 6 exclamation mark equals 720 , the total number of ways to arrange six items.) Each man will sit immediately to the right of a woman. A) There are [blank] ways the given event can occur. B) The probability the given...
In how many ways can three couples be seated in a row so that each couple...
In how many ways can three couples be seated in a row so that each couple sits stogether (namely next to each other): • in a row, 48 48 • in a circle? ? Hint (1 of 1): As in the general comment, recall that rotations matter. It may be useful to imagine a round table with 6 chairs, and a single mark on the table, between two specific chairs. Observe that for some configurations of the 6 people, the...
In how many ways can three couples be seated in a row so that each couple...
In how many ways can three couples be seated in a row so that each couple sits together (namely next to each other) in a circle ? Hint : As in the general comment, recall that rotations matter. It may be useful to imagine a round table with 6 chairs, and a single mark on the table, between two specific chairs. Observe that for some configurations of the 6 people, the mark is between two different couples, denoting the mark...
8&9 8. Four married couples have bought 8 seats in the same row for a concert....
8&9
8. Four married couples have bought 8 seats in the same row for a concert. Ia how manry different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives? 9. A machinist produces 22 items during a shift. Three of the 22 items are defective and the rest are not defective. In how many different orders can the...
discrete math do all please 2. Six people attend the theater together and sit in a...
discrete math do all please
2. Six people attend the theater together and sit in a row with exactly six seats. (a) In how many ways can they be seated together in the row? (b) Suppose one of the six is a doctor who must sit in a specific aisle seat in case she is paged. How many ways can the people be seated together in the row with the doctor in the aisle seat? (c) Suppose the six people...
Please answer 1 and 2 show all work!!!!
1) (6pts) Three married couples have purchased theater tickets and are seated in a row consisting of just six seats. a) How many different seating arrangements are possible? TOTAL: How many different seating arrangéments have the three men (in order) in the three leftmost seats? any b) TOTAL c) Assume the theater-goers take their seats in a completely random fashion. Then each of the seating arrangements in part a) are equally likely....
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events A, [ith couple sit next to each other),-1, 2, 3. Count carefully the numbers of arrangements in...
Exercise 1.52. Three married couples (6 guests altogether) attend a dinner party. They sit at a round table randomly in such a way that each outcome is equally likely. What is the probability that somebody sits next to his or her spouse? Hint. Label the seats, the individuals, and the couples. There are 6! 720 seating arrangements altogether. Apply inclusion-exclusion to the events Ai = (ith couple sit next to each other2, 3. Count carefully the numbers of arrangements in...
Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives?
8. Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives?
In how many ways can three couples be seated in a row so that each couple sits stogether (namely next to each other): • in a row, 48 48 • in a circle? ? Hint (1 of 1): As in the general comment, recall that rotations matter. It may be useful to imagine a round table with 6 chairs, and a single mark on the table, between two specific chairs. Observe that for some configurations of the 6 people, the...
8&9
8. Four married couples have bought 8 seats in the same row for a concert. Ia how manry different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the husbands sit together to the right of all the wives? 9. A machinist produces 22 items during a shift. Three of the 22 items are defective and the rest are not defective. In how many different orders can the...
discrete math do all please
2. Six people attend the theater together and sit in a row with exactly six seats. (a) In how many ways can they be seated together in the row? (b) Suppose one of the six is a doctor who must sit in a specific aisle seat in case she is paged. How many ways can the people be seated together in the row with the doctor in the aisle seat? (c) Suppose the six people...
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