Question

A train is going from Cambridge to London stops at nine intermediate stations. Six persons enter the train during the journey with six different tickets. How many different sets of tickets they have had?

• A. ⁵⁴C₆
• B. ⁵⁵C₆
• C. ⁴⁴C₆
• D. ⁴⁵C₆

Answer 1

The correct option is D

⁴⁵C₆

For $S_1,9$ different tickets available, one for each of the remaining $9$ stations; similarly at $S_2,8$ different tickets are available; and so on.

Hence it is clear, that total no. of different tickets
$=9+8+7+6+5+4+3+2+1=45$

Hence the six different tickets must be any six of these $45;$ and there are evidently as many different sets of $6$ tickets as there are combinations of $45$ things taken $6$ at a time.

Hence the required number $={}^{45}{C}_6=8145060.$