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Four separate awards (excellence in academics, excellence in teaching, excellence in departmental service, excellence in outreach) are given to professors in the Department of Mathematics. There are 50 professors. Find the quantity of possible arrange- ments if:

(i) no person can receive two awards;

(ii) any person can receive any number of awards;

(iii) as in (i), but Mr Smith will not get the teaching award.

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Statistics and Probability, Statistics

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