MP Board · Class 11 · Mathematics · Permutations and CombinationsIf $^nC8 = ^nC2$, find the value of $n$.
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Total Attempts: 5
Accuracy Rate: 40%
Step-by-Step Solution
We know the property of combinations: if $^nC_a = ^nC_b$, then either $a = b$ or $n = a + b$. Here, $8 \neq 2$, so we must have $n = 8 + 2 = 10$. Therefore, option B is correct.
Detailed Options Breakdown
Option : 8
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 1: 10 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: 6
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 3: 12
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.