How many ways can a teacher give 5 different prizes to 5 different of her 25 students
To solve this problem, we can use the concept of permutations.
In this case, the teacher wants to distribute 5 different prizes to 5 different students out of a total of 25 students. Since each student can only receive one prize and the order of the prizes matters, we can use the formula for permutations.
The formula for permutations is:
P(n, r) = n! / (n - r)!
Where "n" represents the total number of items and "r" represents the number of items we want to choose.
In this case, we want to choose 5 students out of 25, so we have:
P(25, 5) = 25! / (25 - 5)!
P(25, 5) = 25! / 20!
Calculating this would require finding the factorial of both 25 and 20. Instead of calculating them manually, we can use a scientific calculator or an online calculator.
By evaluating this expression, we find that P(25, 5) = 25,200 ways.
Therefore, the teacher can give out the 5 different prizes to the 5 different students in 25,200 ways.