Question

Anita invited 10 of her friends, a couple, four men and four women to her anniversary dinner, how many ways Anita can arrange them around a round dinner table

Men insist to sit next to each other

Answer 1

Anita can arrange the guests around the table in 2880 ways.

Step-by-step explanation:

To arrange the guests around the round dinner table, we need to consider the seating arrangement requirements. Anita can arrange the guests around the table in 2880 ways. The four men insist on sitting next to each other. We can treat the couple as one entity.

Then, we can arrange the couple and the four women in a line, which can be done in 5! ways (since there are 5 entities to arrange). Within each entity, the men can be arranged in 4! ways. Therefore, the total number of ways Anita can arrange the guests around the table is 5! × 4!. This equals 120 × 24 = 2880.