import java.math.BigInteger
/*
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:
- BigInteger for safe integer arithmetic
- an efficient binomial coefficient function
- a helper to format numbers with commas
*/
/*
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 BigInteger to avoid overflow.
*/
fun binomial(n: Int, k: Int): BigInteger {
if (k > n) return BigInteger.ZERO
val kk = minOf(k, n - k) // symmetry: C(n, k) = C(n, n-k)
var result = BigInteger.ONE
for (i in 1..kk) {
result = result * BigInteger.valueOf((n - i + 1).toLong()) /
BigInteger.valueOf(i.toLong())
}
return result
}
/*
formatWithCommas(value):
Formats a BigInteger with commas.
*/
fun formatWithCommas(value: BigInteger): String {
val s = value.toString()
return s.reversed().chunked(3).joinToString(",").reversed()
}
fun main() {
val MAIN_COUNT = 5
val MAIN_MAX = 69
val POWER_MAX = BigInteger.valueOf(26)
// Compute C(69, 5)
val mainCombinations: BigInteger = binomial(MAIN_MAX, MAIN_COUNT)
// Multiply by 26 Powerball choices
val totalCombinations: BigInteger = mainCombinations * POWER_MAX
println("Powerball combinations (5 out of 69 and 1 out of 26):")
println("C(69, 5) = ${formatWithCommas(mainCombinations)}")
println("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
*/
