Three out of nine students in the computer club are getting prizes for first, second, and third place in a competition. How many ways can first, second, and third place be assigned? sub 9 cap p sub 3 is equal to the fraction with numerator 9 factorial and denominator open paren 9 minus 3 close paren factorial
First, second, and third place are distinct positions, so order matters. The number of assignments is 9P3 = 9!/(9 − 3)! = 9 × 8 × 7 = 504. Therefore, the correct choice is C, 504.
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