Eleven students are competing in a graphic design contest. In how many different ways can the students finish first, second, and third?There are ways can the students finish first, second, and third.
Question
Eleven students are competing in a graphic design contest. In how many different ways can the students finish first, second, and third?There are ways can the students finish first, second, and third.
Solution
To solve this problem, we use the concept of permutations.
Step 1: Determine the number of ways to choose the first place winner. There are 11 students, so there are 11 ways to choose the first place.
Step 2: Determine the number of ways to choose the second place winner. After the first place is chosen, there are 10 students left, so there are 10 ways to choose the second place.
Step 3: Determine the number of ways to choose the third place winner. After the first and second places are chosen, there are 9 students left, so there are 9 ways to choose the third place.
Step 4: Multiply the number of ways to choose the first, second, and third places. So, 11 * 10 * 9 = 990.
Therefore, there are 990 different ways the students can finish first, second, and third.
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