Question:
In how many ways can 4 girls and 3 boys be seated in a row so that no two boys are together?
Solution:
The seating arrangement would be like this: B G B G B G B G B So, 4 girls
can seat among the four places. Number of ways they can seat is $={ }^{4} \mathrm{P}_{4}=24$ Boys have to seat among the ' $B$ ' areas. So, there are 5 seats available for 3 boys. The number of ways the 3 boys can seat among the 5 places is $={ }^{5} \mathrm{P}_{3}=60$ Therefore, the total number of ways they can seat in this manner is $=(24 \times 60)=1440$.