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 . (Assume all bottles to be alike except for the colour).
My Approach : I used gap method in this. First of all I kept the blue bottles . There is only one way of keeping it , as all are alike . So there are $9$ gaps between blue bottles and I have to place $6$ green bottles (I considered the bottles which are side by side as one.)
So by this my answer is C($9,6$)
But this is wrong…………….Please tell me where I am getting wrong..
Best Answer
After you put 6 of the 7 green bottles in the 9 gaps between the 8 green bottles, you need to put the 7th green bottle in one of the gaps you already picked (since "exactly 1 pair of green bottles is side by side").