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  • 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).

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).

Option: 1

84


Option: 2

360


Option: 3

504


Option: 4

none of these 


Answers (1)

best_answer

First arrange 8 blue alike bottles \rightarrow number of ways = 1 

Now select one gap out of 9 gaps created to put two green bottles \rightarrow number of ways ={ }^9 \mathrm{C}_1

Now select 5 more gaps for other green bottles from remaining 8 gaps \rightarrow number of ways ={ }^8 C_5

Hence, total number of ways 

={ }^9 \mathrm{C}_1 \cdot{ }^8 \mathrm{C}_5=9 \cdot \frac{8 \cdot 7 \cdot 6}{1 \cdot 2 \cdot 3}=504

 

Posted by

Nehul

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