When it comes to forming numbers with three digits, the possibilities may seem endless. But just how many numbers can you actually form? In this blog post, we will explore the mathematical concept of combinations and unveil the total count of three-digit numbers.

Understanding Combinations

In mathematics, combinations refer to the selection of items without regard to the order. In simpler terms, combinations are arrangements where the order does not matter. The formula to calculate combinations is given by:

nCr = n! / r!(n-r)!

Where ‘n’ represents the total number of items and ‘r’ represents the number of items selected.

Applying Combinations to Three-Digit Numbers

Now that we have a basic understanding of combinations, let’s consider its application to three-digit numbers. In this scenario, we have 10 possible digits (0 to 9) to choose from to form each digit of the number.

Calculating the Number of Combinations

Using the formula for combinations, we can determine the number of three-digit numbers possible.

nCr = 10! / 3!(10-3)! = 10! / 3!7! = (10*9*8*7*6*5*4*3*2*1) / [(3*2*1)*(7*6*5*4*3*2*1)]

By simplifying the expression, we get:

nCr = (10*9*8) / (3*2*1) = 120

Therefore, there are 120 possible combinations of three-digit numbers.

A Few Examples

Here are a few examples of three-digit numbers that can be formed:

  • 123
  • 549
  • 876
  • 315

As you can see, the possibilities are vast, ranging from 000 to 999.

In conclusion, when forming three-digit numbers using the digits 0 to 9, there are 120 possible combinations. Combinations provide a mathematical framework to understand and quantify the number of arrangements possible in a given scenario. So, the next time you encounter three-digit numbers, you’ll know just how many variations can be formed!

Let us know if you found this blog post informative and enlightening. Happy number forming!

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