Answer:
36 different ways.
Explanation:
To calculate the number of ways the 3 different algebra books and 3 different physics books can be arranged on a shelf, we can use the concept of permutations.
Permutations refer to the arrangement of objects in a specific order. In this case, we want to arrange the books on a shelf.
To find the total number of arrangements, we can multiply the number of ways to arrange the algebra books by the number of ways to arrange the physics books.
There are 3 algebra books, so the number of ways to arrange them is 3! (read as "3 factorial"). This means we multiply 3 by 2, and then multiply the result by 1. Therefore, there are 3! = 3 x 2 x 1 = 6 ways to arrange the algebra books.
Similarly, there are 3 physics books, so the number of ways to arrange them is also 3!.
To find the total number of arrangements, we multiply the number of ways to arrange the algebra books (6) by the number of ways to arrange the physics books (also 6).
Therefore, the total number of ways to arrange the 3 different algebra books and 3 different physics books on a shelf is 6 x 6 = 36.
In summary, there are 36 different ways to arrange the 3 different algebra books and 3 different physics books on a shelf.