In how many ways can 4 prizes be distributed among 10 students?
Practice Questions
Q1
In how many ways can 4 prizes be distributed among 10 students?
210
5040
10000
1001
Questions & Step-by-Step Solutions
In how many ways can 4 prizes be distributed among 10 students?
Step 1: Understand that we have 4 prizes to give away.
Step 2: Recognize that there are 10 students who can receive these prizes.
Step 3: Realize that the order in which we give the prizes matters (since each prize is distinct).
Step 4: Use the formula for permutations, which is denoted as nPr, where n is the total number of items (students) and r is the number of items to choose (prizes).
Step 5: In this case, n = 10 (students) and r = 4 (prizes), so we need to calculate 10P4.
Step 6: The formula for permutations is nPr = n! / (n - r)!. Here, 10P4 = 10! / (10 - 4)! = 10! / 6!.
Step 7: Calculate 10! (which is 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) and 6! (which is 6 x 5 x 4 x 3 x 2 x 1).
Step 8: Simplify the calculation: 10! / 6! = (10 x 9 x 8 x 7) / 1 = 5040.
Step 9: Conclude that there are 5040 different ways to distribute the 4 prizes among the 10 students.
