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

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=4
n!=6X5x4x3x2x1=720

k!=4x3x2x1=24

n-k=2
Number of combinations=(720/2)/24
=360/24
=15
Working 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 = 6
k = 4
d = n - k
nFac = fac(n)
kFac = fac(k)
dFac = fac(d)
p = (nFac / dFac) / kFac
Debug.Print p

End Sub
Function 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.

[ad_2]

Source by A. Lewis Gibson