In how many ways can 6-girls and 4 boys be seated in a row so that no two boys are together?

No two boys are together.
Step I:  Arrange 6 girls in a row by leaving one seat between every two girls.
            Number of permutations of arranging girls = 6! = 720            ...(i)
        G    G    G    G    G    G     
       1         2        3          4      5        6             7     
Step II:  There are 7 places for the boys to sit in order that no two of them are together.
                     Number of boys = 4
                            n = 7,  r = 4
∴             Number of permutations of arranging boys =  ...(ii)
                Hence, from (i) and (ii),
                 The number of ways in which they may be seated so that no two boys are together
                                                       = 720 x 840 = 604800