Question

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 color)

Answer 1

Answer:

9C6 = 84 ways

Step-by-step explanation:

Consider the two green bottles as one entity. Let's call it GG.

We will also refer to the green bottle as: G, and to the blue bottle as: B.

So now we have 14 units to arrange ( 1 green pair bottle + the remaining 5 green bottles + the 8 blue bottles):

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 we need to take the six green units (the 1 pair and 5 bottles) and place them in six of the nine gaps.

Therefore, the solution is: 9C6 = 84 ways.