There were 24 students running in a race. How many different arrangements of first, second, and third place are possible?
Question
There were 24 students running in a race. How many different arrangements of first, second, and third place are possible?
Solution
To solve this problem, we use the concept of permutations.
Step 1: Identify the number of students running in the race. In this case, there are 24 students.
Step 2: Identify the number of positions to be filled. In this case, we are looking for the number of arrangements for first, second, and third place. So, there are 3 positions to be filled.
Step 3: Use the formula for permutations, which is nPr = n! / (n-r)!. Here, n is the total number of students (24) and r is the number of positions to be filled (3).
Step 4: Calculate the permutation.
24P3 = 24! / (24-3)! = 24! / 21! = 24 * 23 * 22 = 12,144
So, there are 12,144 different arrangements of first, second, and third place possible among 24 students.
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