Question

select the correct answer.
judges at an art competition must select first-, second-, and third-place winners from an exhibition of 12 paintings. in how many different ways can the winning paintings be chosen?
a. 1,320
b. 440
c. 220
d. 18

Explanation:

Step1: Identify the problem type

This is a permutation problem since the order (first, second, third place) matters. The formula for permutations is \( P(n, r)=\frac{n!}{(n - r)!} \), where \( n = 12 \) (total paintings) and \( r = 3 \) (places to choose).

Step2: Apply the permutation formula

Substitute \( n = 12 \) and \( r = 3 \) into the formula:

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Answer:

A. 1,320