Consider a plygon of sides `'n'` which satisflies the equation `3. .^(n)p_(4) = .^(n-1)p_(5)`
Rajdhani express travelling from Delhi to Mumbai has `n` station enroute. Number of ways in which a train can be stopped at `3` stations

Options

A. 20
B. 35
C. 56
D. 84

Answer

D

Explanation

let `a_(0)` be the number of stations to the left of the station I chosen, `a_(1)` be the number of stations between the station I and station II, `a_(2)` be the number of stations between the station II and station III and `a_(3)` be the number of stations to the right of the third station. then,
`a_(0),a_(3) ge 0 and a_(1),a_(2) ge 1`
Also, `a_(0)+a_(1)+a_(2)+a_(3)=n+1-3`
Let `a=a_(0)+1,b=a_(3)+1`, then `a,b ge1` such that
`a+a_(1)+a_(2)+b=n`
`therefore`Required number of ways`=.^(n-1)C_(4-1)=.^(9)C_(3)` [here, `n=10]
=84