Imports System
'---------------------------------------------------------------
' Compute Powerball lottery combinations:
' - Choose 5 distinct numbers out of 69
' - Choose 1 Powerball number out of 26
'
' Total combinations = C(69, 5) * 26
'
' This program:
' - Implements an efficient binomial coefficient function
' - Uses integer arithmetic only
' - Adds comma formatting for readability
'---------------------------------------------------------------
Module PowerballCombinations
'-----------------------------------------------------------
' Binomial(n, k):
' Computes C(n, k) using the multiplicative formula:
'
' C(n, k) = Π (n - i + 1) / i for i = 1..k
'
' This avoids factorial overflow and floating‑point errors.
'-----------------------------------------------------------
Function Binomial(n As Integer, k As Integer) As Long
If k > n Then Return 0
If k > n - k Then k = n - k ' symmetry: C(n,k) = C(n,n-k)
Dim resultValue As Long = 1
For i As Integer = 1 To k
resultValue = resultValue * (n - i + 1) \ i
Next
Return resultValue
End Function
'-----------------------------------------------------------
' FormatWithCommas(value):
' Converts a Long into a comma‑formatted string.
'
' Example:
' 11238513 -> "11,238,513"
'-----------------------------------------------------------
Function FormatWithCommas(value As Long) As String
Return value.ToString("N0") ' built‑in formatting
End Function
Sub Main()
Const MAIN_COUNT As Integer = 5
Const MAIN_MAX As Integer = 69
Const POWER_MAX As Integer = 26
' Compute C(69, 5)
Dim mainComb As Long = Binomial(MAIN_MAX, MAIN_COUNT)
' Multiply by 26 Powerball choices
Dim totalComb As Long = mainComb * POWER_MAX
Console.WriteLine("Powerball combinations (5 out of 69 and 1 out of 26):")
Console.WriteLine("C(69, 5) = " & FormatWithCommas(mainComb))
Console.WriteLine("Total combinations = " & FormatWithCommas(totalComb))
End Sub
End Module
' run:
'
' Powerball combinations (5 out of 69 and 1 out of 26):
' C(69, 5) = 11,238,513
' Total combinations = 292,201,338
'
