For a scholarship, at most n candidates out of 2n + I can be selected. If the number of different ways of selection of at least one candidate is 127, the maximum number of candidates that can be selected for the scholarship is: ?->(Show Answer!)

1. For a scholarship, at most n candidates out of 2n + I can be selected. If the number of different ways of selection of at least one candidate is 127, the maximum number of candidates that can be selected for the scholarship is:

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By: anil on 05 May 2019 02.31 am

At least one candidate and atmost n candidates among 2n+1 candidates => $$^{2n+1}C_1$$ + $$^{2n+1}C_2$$ + ... $$^{2n+1}C_{n-1}$$ + $$^{2n+1}C_n$$ => $$^{2n+1}C_1$$ + $$^{2n+1}C_2$$ + ... $$^{2n+1}C_{n-1}$$ + $$^{2n+1}C_n$$ = 127 n = 3 satisfies the equation. Hence, at most 3 candidates can be selected for scholarship.

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