GRE Permutations & Combinations: Counting Strategies

Counting problems on the GRE are a test of logic, not just formulas. Whether it's a Numeric Entry question or a Quantitative Comparison, success comes from knowing when to multiply, when to add, and when to subtract.

Section 1: The Core Distinction

Foundation: Does Order Matter?

The most critical step is the first one. Learn to distinguish between a 'Selection' (Combination) and an 'Arrangement' (Permutation) using our visual Team vs. Photo scenarios.

The Calculation Method: Slots vs. Formulas

Stop using nPr and nCr formulas blindly. Learn the intuitive 'Countdown Method' (Slot Method) to calculate arrangements and selections faster and with fewer errors.

Section 2: Managing Constraints

Selection Rules: Always vs. Never

Learn how to handle scenarios where specific items MUST be chosen or MUST be excluded from the group.

Arrangement Rules: The 'Glue' Method

How do you seat people if two friends refuse to be separated? Learn the 'Glue' technique to treat multiple items as a single unit.

Arrangement Rules: The Subtraction Strategy

Calculating 'Never Together' directly is messy. Learn the powerful shortcut of subtracting the 'Together' cases from the Total to find the answer instantly.

Handling Repetition: Anagrams

What happens when the items aren't unique (like the letters in MISSISSIPPI)? Learn how to adjust your calculation to account for duplicates.

Section 3: GRE-Specific Strategy

Numeric Entry Shortcut: 'At Least One'

Numeric Entry questions often ask for 'at least one' scenarios. Calculating these directly is slow. Learn the 'Total minus None' shortcut to solve them in seconds.

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