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  • 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.Option: 1</strong

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.

Option: 1

60


Option: 2

54


Option: 3

56


Option: 4

36


Answers (1)

best_answer

B_1 B_2 B_3 \ldots B_7 B_8 B_9 B_{10}

(i) When two terminal books are taken \left(B_1 B_2\right.\text{or} \left.B_9 B_{10}\right) then number of ways =2 \times 7=14
(ii) When two consecutive terminal books are not taken (i.e. \left.B_2 B_3, B_3 B_4, \ldots . B_8 B_9\right)

Then the third book can be selected in 6 ways Then the number of ways are 7 \times 6=42

\therefore \text{Total}=14+42=56\; \text{ways}

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Sayak

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