Question

There is small town railway station and there are 25 stations on that line. At each of the 25 station passenger can get the ticket for any other 24 stations. How many different kinds of tickets do you think the booking clerk has to keep?

Answer 1

each station passengers can get tickets for any of the other 24 stations and,therefore the number of tickets required is 25 x 24 = 600.


i hope it helps you.

Answer 2

Answer:

$600$ different type of tickets booking clerk has to keep.

Step-by-step explanation:

Given 25 railway stations and we have to find the number of tickets from any one station to another station so basically, we have to select 2 stations from the 25 railway stations but here, the arrangement is also needed because the 25 railway stations are in a particular order so the number of permutations possible is:

${ }^{25} P_{2}$

We know that,

${ }^{n} P_{r}=\frac{n !}{(n-r) !}$

Using this relation to expand ${ }^{25} P_{2}$we get,

$\begin{aligned}&{ }^{25} P_{2}=\frac{25 !}{(25-2) !} \\&{ }_{\Rightarrow}{ }^{25} P_{2}=\frac{25 !}{23 !}=\frac{25.24 .23 !}{23 !}\end{aligned}$

In the above equation,$23!$ will be cancelled out from the numerator and denominator we get,

$\begin{aligned}&{ }^{25} P_{2}=\frac{25.24 .1}{1} \\&{ }_{\Rightarrow}{ }^{25} P_{2}=25.24=600\end{aligned}$

Hence, we have calculated 600 single second class tickets that are enable for a passenger to travel from one station to another among 25 railway stations.