A train is going from Mumbai to Pune and make 5 stops on the way. Three persons enter the train after it has started from Mumbai with 3 different tickets. How many different sets of tickets may they have had?Choices:- 15P3 3×15P3 15C3 15C3/3
Question
A train is going from Mumbai to Pune and make 5 stops on the way. Three persons enter the train after it has started from Mumbai with 3 different tickets. How many different sets of tickets may they have had?Choices:- 15P3 3×15P3 15C3 15C3/3
Solution
The answer to this question is 15C3. Here's why:
The problem is asking for the number of different sets of tickets the three people could have. This is a combination problem, not a permutation problem, because the order in which the tickets are purchased does not matter.
The formula for combinations is C(n, r) = n! / [r!(n - r)!], where n is the total number of options (in this case, the 5 stops), r is the number of options chosen at a time (in this case, the 3 tickets), and "!" denotes factorial.
So, we have C(15, 3) = 15! / [3!(15 - 3)!] = 455. Therefore, they could have had 455 different sets of tickets.
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