CBSE · Class 11 · Mathematics · Permutations and CombinationsHow many 3-digit numbers can be formed from the digits 1, 2, 3, 4, and 5 assuming that repetition of the digits is not allowed?
Step-by-Step Solution
The number of ways to arrange 5 distinct digits taken 3 at a time without repetition is given by $^5P_3 = \frac{5!}{(5-3)!} = \frac{5!}{2!} = 5 \times 4 \times 3 = 60$. Therefore, option B is correct.
Detailed Options Breakdown
Option : 125
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 1: 60 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 120
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 3: 20
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
💡 Study Guide: This question tests core syllabus concepts from Permutations and Combinations. For formulas, key summaries, and mock exam reference guides, read the full Permutations and Combinations Revision Notes.