Question: In how many ways can 4 different prizes be awarded to 10 students?
Options:
5040
720
100
40
Correct Answer: 5040
Solution:
The number of ways to award 4 different prizes to 10 students is P(10, 4) = 10! / (10-4)! = 5040.
In how many ways can 4 different prizes be awarded to 10 students?
Practice Questions
Q1
In how many ways can 4 different prizes be awarded to 10 students?
5040
720
100
40
Questions & Step-by-Step Solutions
In how many ways can 4 different prizes be awarded to 10 students?
Correct Answer: 5040
Step 1: Understand that we have 4 different prizes to give out.
Step 2: Recognize that there are 10 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 items (students) and r is the number of items to choose (prizes).
Step 5: In this case, n = 10 (students) and r = 4 (prizes).
Step 6: Plug the values into the formula: P(10, 4) = 10! / (10 - 4)!.
Step 7: Calculate (10 - 4) = 6, so we have P(10, 4) = 10! / 6!.
Step 13: Conclude that there are 5040 different ways to award the 4 prizes to the 10 students.
Permutations – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange a subset of items (prizes) from a larger set (students).
Factorial Notation – The solution involves the use of factorial notation to compute the number of arrangements, which is essential in combinatorial problems.
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