Question

Eight boys and nine girls sit in a row of 17 seats. (a) How many different...

Eight boys and nine girls sit in a row of 17 seats.

(a) How many different seating arrangements are there?

(b) How many different seating arrangements are there if all the boys sit next to each other and all the girls sit next to each other?

(c) How many different seating arrangements are there if no child sits next to a child of the same sex?

Math   Advanced-Math   
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Answer #1

a) There are a total of 8+9=17 people and are there are 17 seats for 17! possible seating arragements

b) All boys can be permuted in 8! ways and the girls in 7! ways. These two groups can be arranged mutually as BG or GB (boys to left or girls to left). So total number of arragements is

c) In this case the boys and girls must alternate. If it starts with a boy then it can be done in ways

If it starts with a girl then again it can be done in ways

So total number of ways is

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!

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