There are 10 students and 10 different books in a classroom. if you assign the students randomly to a book, how many different arrangements could be made?
To solve this problem, we need to use the concept of permutations. A permutation is an arrangement of objects where the order matters.
In this case, we have 10 students and 10 books. We want to find out how many different arrangements can be made when assigning the students to the books. Since each student will take a different book, we need to find the number of permutations of 10 students taken all at a time.
The formula to calculate permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects taken at a time. In our case, n = 10 (number of students) and r = 10 (number of books).
Using this formula, we can calculate the number of arrangements as follows:
10P10 = 10! / (10 - 10)!
= 10! / 0!
= 10!
The exclamation mark (!) represents the factorial of a number, which means multiplying that number by all positive integers less than itself until reaching 1.
Calculating 10!, we get:
10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 3,628,800
Therefore, there are 3,628,800 different arrangements that can be made when assigning the students randomly to the books in the classroom.