Question

1. eleven students are competing in an art contest. in how many different ways can the students finish first, second, and third? (see example 2)

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to find the number of ways to arrange 11 students in 3 distinct positions (first, second, third). The formula for permutations of \( n \) objects taken \( r \) at a time is \( P(n, r)=\frac{n!}{(n - r)!} \). Here, \( n = 11 \) and \( r = 3 \).

Step2: Apply the permutation formula

Substitute \( n = 11 \) and \( r = 3 \) into the formula:

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Step3: Calculate the result

Multiply the numbers: \( 11\times10\times9 = 990 \).

Answer:

990