There are 11 contestants entering a contest to place 1st, 2nd, and 3rd. To calculate the number of possible outcomes, the document uses the permutation formula, where the number of contestants (n) is 11 and the number being arranged (r) is 3. Using the formula nPr = n!/(n-r)!, the number of possible outcomes is calculated to be 11 * 10 * 9 = 990.