Find my way out
1000 people have gathered for a unique competition. As shown, each participant has a very easy task of navigating a grid from start to finish, only walking upwards and rightwards. But there is one condition: no 2 people can choose the same pathway. If a competitor treads on a previously chosen way, he or she will be eliminated.
Below is a preview of a possible path. If were successful among the first participants, what is the chance in % that the runner completes his task?
The answer is 70.
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1 solution
The no of ways one can navigate a grid can be used by the basic theories of permutation.
A person has to take 6 rights and 4 ups in order to complete the grid Thus no of ways of navigating the grid is aranging 6 right and 4 ups
ie, 10! / (6!*4!)=210
given that 63 people were sucessful thus there are still 210-63 ways left =147 ways left
the possibility that the next person is sucessful is given by (147/210)*100
= 70%