Question 1104841
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Kate, who is one of the winners, is one of the 5 contestants, so you need to choose 2 of the other 4 to be the other two winners.  The number of ways of doing that is "4 choose 2" = {{{4!/((2!)(2!)) = 6}}}.<br>
Then the three winners can get the gold, silver, and bronze awards in any of 3!=6 orders.<br>
So the total number of permutations, given that Kate is one of the three winners, is 6*6 = 36.