In how many ways can 8 people be seated in a row if a.) there are no restrictions on the seating arrangement(answer is 8! = 40,320) , b.) persons A and B must sit next to each other? (Answer: 10,080) , c.) there are 4 men and 4 women and no 2 men or 2 women can sit next to each other? (Answer: 1,152) , d.) there are 5 men and they must sit next to one another? (Answer: 2,880) , e.) there are 4 married couples and each couple must sit together? (Answer: 384). I need to see the steps to solve questions 10b to 10e. I quickly looked through the corresponding chapter on combinatorial analysis and I went over topics such as the multinomial theorem, the basic principle of counting, the binomial theorem, and representing the number of possible combinations of n objects taken r at a time as "n choose r" .

Question

In how many ways can 8 people be seated in a row if a.) there are no restrictions on the seating arrangement(answer is 8! = 40,320) , b.) persons A and B must sit next to each other? (Answer: 10,080) , c.) there are 4 men and 4 women and no 2 men or 2 women can sit next to each other? (Answer: 1,152) , d.) there are 5 men and they must sit next to one another? (Answer: 2,880) , e.) there are 4 married couples and each couple must sit together? (Answer: 384). I need to see the steps to solve questions 10b to 10e. I quickly looked through the corresponding chapter on combinatorial analysis and I went over topics such as the multinomial theorem, the basic principle of counting, the binomial theorem, and representing the number of possible combinations of n objects taken r at a time as "n choose r" .

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