In how many ways can 5 boys and 3 girls be arranged so that no two girls will sit side by side.

Explanation

5 boys can be arranged among themselves in `5!` ways. As no 2 girls sit side by side, they can be seated in the gaps between any two boys. here the number of gaps=6. `therefore` Number of ways of placing girls = `^6P_3=(6xx5xx4xx3xx2)/(3xx2)=120. `therefore` Required number of ways = `1220xx5!= 120xx120= 14400`.