Question

On a railway route, there are $15$ stations. The number of tickets required in order that is may be possible to book a passenger from every station to every other is

• A. $105$
• B. $210$
• C. $15!$
• D. $\frac{15!}{2!}$

Answer 1

Answer: (B)

$210$

There are total 15 stations .

Let name them as A,B,C......O

If anyone want to travel from A to B,C,D,E......O then there will be 14 ticket required,

Now from B station to C,D,E....O then there will be 13 ticket required

In the same it will go until 1 ticket will be required

So the total tickets required will be =$14+13+12+11+...1=\frac{14\times 15}{2}\left(\frac{n(n+1)}{2}\right)=105$

But for both way double tickets will be required .

So total tickets =$105\times 2=210$

Correct option is B