In how many ways can 10 boys and 10 girls sit in a row so that no two boys sit together ?

Explanation

10 boys and 10 girls sit in a row so that no two boys sit together. So a boy is to be seated between two girls or at the two ends of the row. So the boys are to be seated in 11 positions in `""^11C_10` ways. Again 10 boys and 10 girls can be arranged among themselves in 10! and 10! ways respectively. `:."The total number of ways = ""^11C_10xx10! xx10! =(11)! xx (10)!`