first the assumptions: all are seated in one row on 11 seats, adults and children are non differentiated if switched places. Then:
4 children take the side seats and we are left just with the 6 adilts and the old chap on 7 seats. now only difference is where the old one sits. he can be seated on 5 different places (not on side seats by the children). So answer is 5.
If each child and adults are all considered different, then 4-children 4 places=4!=24. 6 adults 6 places = 6!=720 and the old one -5. so total 24*720*5=a lot!