In this race 1st, 2nd, and the 3rd places can be awarded in 1320 different ways.
What is permutation?
The different ways of arranging the elements of a set is called permutation.
Here, in this given question 12 runners are competing.
The different ways first, second, and third place trophies be awarded among 12 runners is = ¹²P₃ = 12! / (12 - 3)! = 12! / 9!
= (12 × 11 × 10 × 9!) / 9! = 12 × 11 × 10 = 1320.
Hence, in different 1320 ways 12 runners can be awarded for the 1st, 2nd and 3rd places.
Learn more about permutation here: https://brainly.com/question/23283166
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