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  • A meeting with 10 teachers will take place in a conference hall. How many different ways these teachers could be seated around a round table if 4 of them always was seated together?<d

A meeting with 10 teachers will take place in a conference hall. How many different ways these teachers could be seated around a round table if 4 of them always was seated together?

Option: 1

1920


Option: 2

2160


Option: 3

2880


Option: 4

3240


Answers (1)

best_answer

We can arrange the 4 boys in 4 ! =24  ways. Then, we can insert the 4 girls into the 5 spaces between the boys, in any order, in 5 !  ways. However, for each of these arrangements, the two end spaces cannot be occupied by girls. Therefore, we must subtract the arrangements where a girl is in one of the two end spaces. There are 2 ways to select which end space is occupied, and 4 ! \times 4 ! ways to arrange the boys and girls in the remaining spaces. Therefore, the total number of ways is 4 ! \times 5 ! \times-2 \times 4 ! \times 4 !=1920

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