Number of ways in which 7 green bottles and 8 blue bottles can be arranged in a row if exactly 1 pair of green bottles is side by side, is (Assume all bottles to be alike except for the colour):

G G G G G G G/B B B B B B B B One gap out of nine can be taken in 9C1 ways and 2 green bottles can be placed. Now, green remaining 5Gaps remaining 85 gaps out of 8 gaps for remaining 5 green bottles can be selected in 8C5 .  Hence, total ways =9C18C5=9⋅8.7.61.2.3=72.7=504