Homework
There are In how many ways can the digits in the number be arranged?

To find the number of ways to arrange the digits in the number , you first note that it has 8 digits and includes repetitions: the digit ‘5’ appears 2 times and the digit ‘1’ also appears 2 times. The formula for arranging n items where there are repeats is given by:

In this case, we have:

So, the calculation is:

Thus, there are ways to arrange the digits in the number .

Now, let’s dig into some interesting facts!

Did you know that the arrangement of numbers is not just for academics but has real-life applications too? For instance, arranging digits is common in coding theory, where you might need distinct combinations to create secure passwords. The world of computer algorithms often utilizes these arrangements to optimize processes like sorting and searching!

When working on problems like this, it’s always good to keep track of repeating elements. A common mistake is to forget to divide by the factorial of the frequency of repeated digits, which can considerably inflate the total arrangements. Always double-check if your items have duplicates before calculating the total!