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There are 10 different books in a shelf....

There are `10` different books in a shelf. The number of ways in which three books can be selected so that exactly two of them are consecutive is

A

A. `60`

B

B. `54`

C

C. `56`

D

D. `36`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` `B_(1)B_(2)B_(3)…B_(7)B_(8)B_(9)B_(10)`
`(i)` When two terminal books are taken (`B_(1)B_(2)` or `B_(9)B_(10)`) then number of ways `=2xx7=14`
`(ii)` When two consecutive terminal books are not taken (i.e.`B_(2)B_(3)`,`B_(3)B_(4)`,……..`B_(8)B_(9)`)
Then the third book can be selected in `6` ways
Then the number of ways are `7xx6=42`
`:.` Total `=14+42=56` ways
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