Question

Number of ways in which $7$ green bottles and $8$ blur 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).

• A. $814$
• B. $84$
• C. $504$
• D. $85$

Answer 1

The correct option is B $84$

Consider $2$ green bottles as $1$ entity(GG)

Let green bottle G, blue bottle B.

So now we have $14$ units to arrange.

GG, G, G, G, G, G, B, B, B, B, B, B, B, B

Now place the $8$ blue bottles in a row such that between each bottle has a gap before and after it.

-B-B-B-B-B-B-B-B-

Now take $6$ green units and place in $6$ of $9$ gaps.

So ${}^9{C}_6=84$ ways.