In how many ways can 4 different prizes be awarded to 3 students?
Practice Questions
1 question
Q1
In how many ways can 4 different prizes be awarded to 3 students?
12
24
36
48
The number of ways is P(4, 3) = 4! / 1! = 24.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 4 different prizes be awarded to 3 students?
Solution: The number of ways is P(4, 3) = 4! / 1! = 24.
Steps: 9
Step 1: Understand that we have 4 different prizes and 3 students.
Step 2: Realize that we need to award the prizes to the students, and each student can receive only one prize.
Step 3: Identify that we are looking for the number of ways to choose 3 prizes from the 4 available prizes.
Step 4: Use the formula for permutations since the order in which the prizes are awarded matters. The formula is P(n, r) = n! / (n - r)!, where n is the total number of items (prizes) and r is the number of items to choose (students).
Step 5: In this case, n = 4 (prizes) and r = 3 (students). So we calculate P(4, 3).
Step 6: Substitute the values into the formula: P(4, 3) = 4! / (4 - 3)! = 4! / 1!.
Step 7: Calculate 4! (which is 4 x 3 x 2 x 1 = 24) and 1! (which is 1).
Step 8: Divide 24 by 1 to get the final answer: 24.
Step 9: Conclude that there are 24 different ways to award the 4 prizes to the 3 students.
