/*
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:
- u128 for safe integer arithmetic
- an efficient binomial coefficient function
- a helper to format numbers with commas
*/
/// 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 inaccuracies.
fn binomial(n: u128, k: u128) -> u128 {
if k > n {
return 0;
}
// Use symmetry: C(n, k) = C(n, n-k)
let k = if k > n - k { n - k } else { k };
let mut result: u128 = 1;
for i in 1..=k {
result = result * (n - i + 1) / i;
}
result
}
/// Formats a u128 with commas.
/// Example: 11238513 -> "11,238,513"
fn format_with_commas(value: u128) -> String {
let s = value.to_string();
let mut out = String::new();
let mut count = 0;
for ch in s.chars().rev() {
if count == 3 {
out.push(',');
count = 0;
}
out.push(ch);
count += 1;
}
out.chars().rev().collect()
}
fn main() {
const MAIN_COUNT: u128 = 5;
const MAIN_MAX: u128 = 69;
const POWER_MAX: u128 = 26;
// Compute C(69, 5)
let main_combinations: u128 = binomial(MAIN_MAX, MAIN_COUNT);
// Multiply by 26 Powerball choices
let total_combinations: u128 = main_combinations * POWER_MAX;
println!("Powerball combinations (5 out of 69 and 1 out of 26):");
println!("C(69, 5) = {}", format_with_commas(main_combinations));
println!("Total combinations = {}", format_with_commas(total_combinations));
}
/*
run:
Powerball combinations (5 out of 69 and 1 out of 26):
C(69, 5) = 11,238,513
Total combinations = 292,201,338
*/
