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

Monjur Alahi

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).
A. `84`
B. `360`
C. `504`
D. none of these


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Salim Ahmed Kawsar

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Correct Answer - C
`(c )` First arrange `8` blue alike bottles `to ` number of ways `=1`
Now select one gap out of `9` gaps created to put two green bottles `to `number of ways `=.^(9)C_(1)`
Now select `5` more gaps for other green bottles from remaining `8` gaps `to` number of ways `=.^(8)C_(5)`
Hence, total number of ways
`=.(9)C_(1)*^(8)C_(5)=9*(8*7*6)/(1*2*3)=504`

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