Question

There are 9 boys and 5 girls. find the no. of ways in which they can be seated in a row so that all the boys do not sit together

Answer 1

There are 20 of these cases. For each of these, there are 3=63=6 ways to arrange the boys and 5=1205=120 ways to arrange the girls. This gives us a total of 20⋅6⋅120=1440020⋅6⋅120=14400