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Out of 2n+1 students, n students have to be given the scholarships. The number of ways in which at least one student can be given the scholarship is 63. What is the number of students receiveing the scholarship?

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A child studying hard for the sake of getting a scholarship is an example of

There are 5 candidates for mathematics , 7 for science and 3 for arts scholarship . Find the number of ways of give one scholarship either for mathematics or for science or for arts.

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There are 3 condidates for a Classical; 5 for a Mathematical and 4 for a Natural science scholarship.(i) In how many ways can these scholarship be awarded? (ii) In how many ways one of these scholarships be awarded?