Combinatorics Mental Math Shortcuts
Combinatorics mental math shortcuts for cancellation, small combinations, symmetry, factorial simplification, and counting checks.
Candidates who can set up combinations but struggle to compute them.
Cancel early
Combination formulas often contain large factorials that cancel. Expand only the needed terms and reduce before multiplying.
Use symmetry
n choose k equals n choose n minus k. Computing 10 choose 8 as 10 choose 2 is much easier and avoids unnecessary arithmetic.
Concrete example
For 8 choose 3, compute 8 x 7 x 6 divided by 3 x 2 x 1. Cancel 6 with 3 x 2, leaving 8 x 7 = 56 without multiplying large factorials.
Memorize small values
Know small combinations like 5 choose 2, 6 choose 3, and 10 choose 2. These appear often enough to justify automatic recall.
Common mistakes
Candidates often calculate correctly from the wrong setup. Shortcuts help only after order, replacement, and grouping are defined.
Practice the pattern
Use the LeetQuidity curriculum and calibration to turn this topic into a focused practice plan.