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In how many ways can 3 different prizes be awarded to 5 students?
In how many ways can 3 different prizes be awarded to 5 students?
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In how many ways can 3 different prizes be awarded to 5 students?
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The number of ways to award 3 different prizes to 5 students is P(5, 3) = 5! / (5-3)! = 60.
Questions & Step-by-step Solutions
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Q: In how many ways can 3 different prizes be awarded to 5 students?
Solution:
The number of ways to award 3 different prizes to 5 students is P(5, 3) = 5! / (5-3)! = 60.
Steps: 9
Show Steps
Step 1: Understand that we have 3 different prizes to give out.
Step 2: Recognize that there are 5 students who can receive these prizes.
Step 3: Realize that the order in which we award the prizes matters because they are different.
Step 4: Use the formula for permutations, which is P(n, r) = n! / (n - r)!, where n is the total number of students and r is the number of prizes.
Step 5: In this case, n = 5 (students) and r = 3 (prizes).
Step 6: Plug the values into the formula: P(5, 3) = 5! / (5 - 3)!.
Step 7: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120) and (5 - 3)! (which is 2! = 2 x 1 = 2).
Step 8: Now divide: 120 / 2 = 60.
Step 9: Conclude that there are 60 different ways to award the 3 prizes to the 5 students.
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