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A train is going from cambridge to londo...

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?

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The correct Answer is:
`.^(45)C_(6)`

For `S_(1),9` different tickets are available, one for each of the remaining 9 stations, similarly at `S_(2)`,8 different tickets are available and so on.
thus, total number of different tickets
`=9+8+7+6+5+4+3+2+1=45`
so, 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)`.
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