/*
This program computes the total number of Powerball lottery combinations:
- Choose 5 distinct numbers out of 69
- Choose 1 Powerball number out of 26
Total combinations = C(69, 5) * 26
It uses:
- BigInt for safe integer arithmetic
- an efficient binomial coefficient function
- a helper to format numbers with commas
*/
object PowerballCombinations {
/*
binomial(n, k):
Computes C(n, k) using the multiplicative formula:
C(n, k) = Π (n - i + 1) / i for i = 1..k
Implemented using BigInt to avoid overflow.
*/
def binomial(n: Int, k: Int): BigInt = {
if (k > n) return BigInt(0)
val kk = math.min(k, n - k) // symmetry: C(n, k) = C(n, n-k)
var result = BigInt(1)
for (i <- 1 to kk) {
result = result * BigInt(n - i + 1) / BigInt(i)
}
result
}
/*
formatWithCommas(value):
Formats a BigInt with commas.
*/
def formatWithCommas(value: BigInt): String = {
val s = value.toString
s.reverse.grouped(3).mkString(",").reverse
}
def main(args: Array[String]): Unit = {
val MAIN_COUNT = 5
val MAIN_MAX = 69
val POWER_MAX = 26
// Compute C(69, 5)
val mainCombinations: BigInt = binomial(MAIN_MAX, MAIN_COUNT)
// Multiply by 26 Powerball choices
val totalCombinations: BigInt = mainCombinations * POWER_MAX
println("Powerball combinations (5 out of 69 and 1 out of 26):")
println(s"C(69, 5) = ${formatWithCommas(mainCombinations)}")
println(s"Total combinations = ${formatWithCommas(totalCombinations)}")
}
}
/*
run:
Powerball combinations (5 out of 69 and 1 out of 26):
C(69, 5) = 11,238,513
Total combinations = 292,201,338
*/
