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GATE CSE 2025 Session 1 Q10: Ways to buy 3 scoops from 4 flavours

Question

A shop has 4 distinct flavors of ice-cream. One can purchase any number of scoops of any flavor. The order in which the scoops are purchased is inconsequential.

If one wants to purchase 3 scoops of ice-cream, in how many ways can one make that purchase?

Try it: multiple choice: exactly one correct option

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Wrong answer costs 2/3 mark in GATE.
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Answer: B (official GATE 2025 final answer key)

Concept used: Combinations with repetition (stars and bars).

First step: Choosing 3 items from 4 types with repetition gives (3+4−13)=(63)\binom{3 + 4 - 1}{3} = \binom{6}{3}.

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Source: official GATE 2025 Session 1 CS question paper and final answer key, organised by IIT Roorkee. Question paper · Answer key

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