Question

A train is going from London to Cambridge stops at 12 intermediate stations. 75 persons enter the train during the journey with 75 different tickets of the same class. Number of different sets of tickets they may be holding is

• A. ${}^{78}{C}_3$
• B. ${}^{91}{C}_{75}$
• C. ${}^{84}{C}_{75}$
• D. none

Answer 1

Answer: (A)

${}^{78}{C}_3$

A Person starting from London will have $13$ options.

Also the next person who starts at 2nd station will have $12$ options.

So, total number of options $\sum 13=78$ and number of people $=75$

$\therefore$ number of different set of tickets

${{}^{78}C}_{75}$ or ${{}^{78}C}_{78-75}$

$={{}^{78}C}_3.$

Hence, the answer is ${{}^{78}C}_3.$