How To Calculate The Number Of Possible Combinations In A Lottery Application

# How To Calculate The Number Of Possible Combinations In A Lottery Application

Latest Casino News 10 Apr , 2017 0

One of the difficulties in generating lotto numbers is knowing the amount of combinations needed to cover all the potential winners.

Calculating Possible Combinations In A Lottery Draw

The formula is taken directly from probability theory and makes use of the factorial method. A factorial is simply a number multiplied by lesser numbers down to one.

```So, the factorial of 4 is 4x3x2x1=24 and is written as 4!
```

Here's the general formula for working out the amount of combinations in any given set of numbers.

```Number of Combinations=(n!/(n-k)!)/k!Where n is all the numbers available to choose from and k is how many in each combination.
```

Let's take a simple sports example to explain this further.

If there are 6 players to choose from, how many possible teams of 4 players are there?

```Working through our formula
n=6, k=4n!=6X5x4x3x2x1=720
k!=4x3x2x1=24
n-k=2Number of combinations=(720/2)/24=360/24=15Working this out manually we get the 15 combinations.1234
1235
1236
1245
1246
1256
1345
1346
1356
1456
2345
2346
2356
2456
3456
```

Using An Excel Formula To Calculate The Possible Lottery Combinations

With a lottery application, it's likely the numbers will be larger so you might need a more efficient way of calculating the formula.

With Excel, you can use the following:

```=COMBIN(n,k)So typing =combin(6,4) in any cell should give an output of 15
```

Creating A Function In VBA To Calculate Lotto Combinations

Using VBA to do the same calculation is a little more complex; because there is no factorial function in Visual Basic, you need to create your own.

Here's an example.

```n = 6
factorial = n
For x = 5 To 1 Step -1
factorial = factorial * x
Next
Debug.Print factorial
```

To apply the formula in VBA you would probably wrap the factorial code is a separate function.

```Sub test1()n = 6k = 4d = n - knFac = fac(n)kFac = fac(k)dFac = fac(d)p = (nFac / dFac) / kFacDebug.Print p
End SubFunction fac(j)
factorial = j
For x = j - 1 To 1 Step -1
factorial = factorial * x
Next
fac = factorial
End Function
```

The VBA code is complex, compared to the simplicity of the Excel formula but it's likely that to create a flexible lotto application you'll need some calculations done directly in code.

Summary

This article has shown one method of calculating the number of combinations in a lottery draw. While some players work out the formula manually, it's good idea to know how to automate the task, ensuring any lotto application has the flexibility required.