GATE 2026 CY – Question 4
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
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Correct answer: (B) 24
Explanation
The single-digit prime numbers are 2, 3, 5 and 7, so there are 4 of them.
We need 3-digit numbers made from **three distinct** primes from these four.
- **Hundreds place:** any of the 4 primes.
- **Tens place:** any of the remaining 3.
- **Units place:** any of the remaining 2.
$$4\times3\times2=\mathbf{24}.$$
(Equivalently, $\binom43\times3!=4\times6=24$.)