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?

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Solution

Step-by-step verified solution

Official answer: B) 20

Quantitative Aptitude

This problem corresponds to finding the number of combinations with repetition (multiset combinations or the stars and bars problem).

We need to select $r = 3$ scoops from $n = 4$ distinct flavors where repetition is allowed and order does not matter.

The formula for combinations with repetition is:

\binom{n + r - 1}{r}

Substituting $n = 4$ and $r = 3$ :

\binom{4 + 3 - 1}{3} = \binom{6}{3} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20

Thus, there are 20 ways to make the purchase, which corresponds to option (B).

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This Quantitative Aptitude previous year question is Q10 of the GATE CSE 2025 Set 1 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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Quantitative Aptitude in GATE CSE

Quantitative Aptitude has 53 GATE CSE PYQs across 13 papers from 2011 to 2026. 27 of them are 2-mark MCQs like this one, and GATE CSE 2025 Set 1 has 4.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.