Non-consecutive Lotto

What this combinatorial lotto counting question tests

This is a hard combinatorics problem that requires careful setup and the principle of complementary counting. It appears in quant interviews as a test of whether you can translate a constraint (consecutive numbers) into a tractable counting argument, rather than enumerate by brute force.

The question rewards candidates who recognize that it's often easier to count the complement—in this case, combinations that satisfy a stricter property—and then subtract. You'll need to think about how to characterize and enumerate valid configurations, then apply combinatorial formulas accurately. The final answer is a specific integer, so precision in both logic and arithmetic matters.

• Complementary counting and inclusion–exclusion
• Constraints on combinatorial objects (consecutive elements)
• Bijection and recurrence-based counting techniques