GATE CSE 2021 Set 1 Q8: Probability that at least two of five picked chocolates match

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.

The probability that at least two chocolates are identical is ___________

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: C (official GATE 2021 final answer key)

Concept used: Complement rule (birthday problem): P(at least two equal) = 1 − P(all distinct).

First step: P(all five different) $= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6}{10^5}$ .

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Source: official GATE 2021 Set 1 CS question paper and final answer key, organised by IIT Bombay. Question paper · Answer key