Answer:
1440 ways
Step-by-step explanation:
- For the math books, there are 5 different books, so there are 5! ways to arrange them.
- For the science books, there are 3 different books, so there are 3! ways to arrange them.
- For the English books, there are 2 different books, so there are 2! ways to arrange them.
Let's solve
5! = 5 × 4 × 3 × 2 × 1 = 120
3! = 3 × 2 × 1 = 6
2! = 2 × 1 = 2
120 × 6 × 2 = 1440 ways
So, there are 1440 different ways you can arrange the math, science, and English books.
There are 3,628,800 different ways to arrange 5 math books, 3 science books, and 2 English books, as the calculation is based on the factorial of the total number of books, which is 10!, amounting to 3,628,800 arrangements.
To determine the number of different ways you can arrange 5 different math books, 3 different science books, and 2 different English books on a shelf, you apply the principle of permutations.
The total number of books is 10 (5 math + 3 science + 2 English), and since each book is different, you will use the factorial function to find the number of permutations. Factorial, denoted by an exclamation mark (!), is the product of all positive integers up to a given number. Here, you need to calculate 10!, which is 10×9×8×7×6×5×4×3×2×1.
This calculation may seem daunting, but with a calculator or a computational tool, you can easily find that 10! equals 3,628,800. Therefore, there are 3,628,800 different ways to arrange the total set of books.
