Question:
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
How many 3-digit numbers can be formed using three distinct single digit prime numbers?
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Count how many single-digit primes exist, then work out how many ways the three digit positions can each independently be filled from that set.
Updated On: Jul 17, 2026
- 64
- 24
- 12
- 4
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Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Identify the digits available. The single-digit prime numbers are 2, 3, 5, and 7, since these are the only prime numbers less than 10. This gives a pool of 4 distinct digits to choose from.
Step 2: Interpret the counting rule for forming 3-digit numbers. The problem asks for 3-digit numbers formed using these single digit primes, with each of the three digit positions filled independently from the pool of 4 available primes.
Step 3: Count the number of ways to fill the three positions. Each of the 3 positions (hundreds, tens, units) can independently take any of the 4 prime digits, since every digit in the set {2, 3, 5, 7} is nonzero and therefore valid in every position including the leading position. This gives a total count of 4 x 4 x 4 = 64 distinct 3-digit numbers.
Step 4: Conclude. The total number of 3-digit numbers that can be formed is 64.
\[ \boxed{64} \]
Step 2: Interpret the counting rule for forming 3-digit numbers. The problem asks for 3-digit numbers formed using these single digit primes, with each of the three digit positions filled independently from the pool of 4 available primes.
Step 3: Count the number of ways to fill the three positions. Each of the 3 positions (hundreds, tens, units) can independently take any of the 4 prime digits, since every digit in the set {2, 3, 5, 7} is nonzero and therefore valid in every position including the leading position. This gives a total count of 4 x 4 x 4 = 64 distinct 3-digit numbers.
Step 4: Conclude. The total number of 3-digit numbers that can be formed is 64.
\[ \boxed{64} \]
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