(A) Let the $10$ intermediate stations be $S_1, S_2, S_3, \dots, S_{10}$.We need to select $3$ stations such that no two are consecutive.This is a cla

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(A) Let the $10$ intermediate stations be $S_1, S_2, S_3, \dots, S_{10}$.We need to select $3$ stations such that no two are consecutive.This is a classic problem of selecting $r$ objects from $n$ objects arranged in a row such that no two are consecutive,which is given by the formula $^{n-r+1}C_r$.Here,$n = 10$ and $r = 3$.Number of ways $= ^{10-3+1}C_3 = ^8C_3$.Calculating the value: $^8C_3 = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$.

Class 11 Mathematics Permutations and Combinations Definition of combinations, Condition combinations

Medium

There are $10$ intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at $3$ of these intermediate stations so that no two of these halting stations are consecutive is:

AP EAMCET 2017 All AP EAMCET

A
$56$
B
$20$
C
$126$
D
$120$

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Permutations and Combinations

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Definition of combinations, Condition combinations

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There are $10$ intermediate stations on a railway line between two particular stations. The number of ways that a train can be made to stop at $3$ of these intermediate stations so that no two of these halting stations are consecutive is:

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