In a network of railways, a small island has $15$ stations. Find the number of different types of tickets to be printed for each class, if every stations must have tickets for other stations.

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Solution

For each pair of stations, two different types of tickets are required.

Now, the number of selections of $2$ stations from $15$ stations $=$ $^{15} C_{2}$ .

$∴$ Required number of types of tickets $= 2$

$^{15} C_{2} = 2 \frac{15!}{2! 13!}$ $= 15 \times 14 = 210$ .

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In a network of railways, a small island has 15 stations. Find the number of different types of tickets to be printed for each class, if every stations must have tickets for other stations.

For each pair of stations, two different types of tickets are required.Now, the number of selections of 2 stations from 15 stations = 15C2.∴ Required number of types of tickets =2 15C2=215!2!13! =15×14=210.

In a network of railways, a small island has $15$ stations. Find the number of different types of tickets to be printed for each class, if every stations must have tickets for other stations.

For each pair of stations, two different types of tickets are required.

Now, the number of selections of $2$ stations from $15$ stations $=$ $^{15} C_{2}$ .

$∴$ Required number of types of tickets $= 2$

$^{15} C_{2} = 2 \frac{15!}{2! 13!}$ $= 15 \times 14 = 210$ .