Question

A teacher has 15 students in his class, 8 girls and 7 boys. He wants to seat them in three rows of five, but knows that if any row has two girls or two boys sitting next to each other, they will talk and won't pay attention. How many seating arrangements can he make that avoid this

Answer 1

609638400

Explanation:

Each row must alternate boys and girls, so every row is either BGBGB or GBGBG, where B denotes a boy and G denotes a girl. Since there are 8 girls and 7 boys, the teacher must have two rows of GBGBG and one row of BGBGB. There are three ways to choose this row, and once this is done, every seat is reserved for either a girl or a boy. There are 8! ways to arrange the girls in their seats, and 7! ways to arrange the boys, so the total number of seating arrangements is 3 * 7! * 8!

Answer 2

609638400

Explanation: