Question

Rajdhani Express going from Bombay to Delhi stops at five intermediate stations, $10$ passengers enter the train during the journey with $10$ different ticket of two classes.The number of different sets of tickets they may have is

• A. ${}^{15}{C}_{10}$
• B. ${}^{20}{C}_{10}$
• C. ${}^{30}{C}_{10}$
• D. None of these

Answer 1

The correct option is C ${}^{30}{C}_{10}$

$2$ classes are there, assume it class $1$ and $2.$

Suppose passenger enters $0+A$, he has $5$ options either $B,C,D,E$ or Delhi.

Similarly for $B$ we have $4$ and for all others we can think.

Also options will depend on class as we have $2$ choices for each,

Total choice $=5+4+3+2+1$

$=15\times 2$ $\to$ taking class.

$=30.$

Now, these are no of tickets while passengers are $10$

So, no. of ways ${}^{30}{C}_{10}.$

Hence, the answer is ${}^{30}{C}_{10}.$