Probability problems reduce to counting when outcomes are equally likely.

Key counting formulas:

• Permutations (order matters): nPr = n!/(n-r)!
• Combinations (order doesn't matter): nCr = n!/(r!(n-r)!)
• With replacement, ordered: $n^r$ choices
• Identical objects distribution: (n+r-1)C(r-1) [stars and bars]

Common setups in JEE:

• Drawing balls from a bag → combinations (unordered)
• Arranging people → permutations (ordered)
• Dice/coin throws → with replacement ($n^r$ total outcomes)
• Card problems → combinations from 52-card deck

Tip: Always identify whether sampling is with/without replacement and whether order matters before counting.