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Twenty students compete in a programming competition in which the top four students are recognized with trophies for first, second, third, and fourth places. How many different outcomes are there for the top four places? The judges decide that they will award honourable mention certificates to four individuals who did not receive trophies. In how many ways can the honourable mention recipients be selected (after the top four places have been determined)? How many total outcomes (trophies and certificates) are there then?

math   Statistics-And-Probability   
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Answer #1

1)number of different outcomes for top four places =20*19*18*17 =116280

2) number of ways the honourable mention recipients be selected =16*15*14*13 =43680

3) total outcome =116280*43680 =5079110400

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