Consider a polygon of sides 'n' which satisfies the equation `3*.^(n)P_(4)=.^(n-1)P_(5)`.
Q. Rajdhani express travelling from Delhi to Mumbai has n stations enroute. Number of ways in which a train can be stopped at 3 stations if no two of the stopping stations are consecutive, is

Options

A. If no two of the stopping are consecutive, is `56`
B. If no two of the stopping are consecutive, is `35`
C. If all the three stopping stations are consecutive, is `18`
D. If all the three stopping stations are consecutive, is `17`

Answer

A

Explanation

`3.(n!)/((n - 4)!) = ((n - 1)!)/((n - 6)!), 3n = (n - 4)(n - 5)`
`rArr 3n = n^(2) - 9n + 20 rArr b^(2) - 12n + 20 = 0`
`n = 10, n = 2` , not possible
so `n = 10`
Delhi `I_(1) , I_(2) , I_(3) , I_(4) ……. I_(10)` Mumbai
`3` intermediate station such that no two are consecutive
Train is stopping at `3` station, for `7` remaining station there are `8` gaps.
Filling these `3` station out of `8` gaps can be done in `.^(8)C_(3) = 56` ways