NCERT · Class 11 · Mathematics · Permutations and CombinationsIn how many ways can a committee of 3 persons be chosen out of 8 persons?
Step-by-Step Solution
The number of ways to choose 3 persons out of 8 is given by the combination $^8C_3 = \frac{8!}{3!(8-3)!} = \frac{8!}{3!5!} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56$. Therefore, option C is correct.
Detailed Options Breakdown
Option : 336
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 1: 112
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 2: 56 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: 24
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.