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 ${}^{30}{C}_{10}$

For a particular class the total number of different tickets from first intermediate station is $5$.

Similarly, number of different tickets from second intermediate station is $4$.

So the total number of different tickets for particular class is
$5+4+3+2+1=15$.

Similarly, same number of tickets will be available for another class also.
Hence number of different tickets available for both class in jouney is equal to $30$

$\therefore$number of ways of selecting $10$ tickets from $30$ is ${}^{30}{C}_{10}$