# Twelve students compete in a race. In how many ways first three prizes be given?

Given: A total of three prizes are to be given.

Number of ways to select the winner of the first prize is 12C1

Number of ways to select the winner of the second prize is 11C1 (11 since one student is already given a prize)

Number of ways to select the winner of the third prize is 10C1 (10 since two students are already given a prize)

Hence, total number of ways is 12C1 × 11C1 × 10C1 = 12 × 11 × 10 = 1320

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