gopal n viv,

hey ur methods r wrong. coz  by usin 7p6, u r includin cases where 1st gap is chosen, 2nd gap is missed n remaining gaps r chosen

heres the correction.

 _g1_g2_g3_g4_g5_g6_

there are cases in wich girls are seated together in ur method.

now subtract cases in wich girls are seated together.

 say fix a girl in pos1 now 5 girls can sit adjacent to her and remaining people can permute in 6!*6! times.

so suybtract 5*6!*6! from da ans u got, i.e 7*6!*6!

so ans is 2*6!*6!

so ans gvn is correct

 

nudge if doubtful,

rate if useful