MP Board · Class 11 · Mathematics · Permutations and CombinationsEvaluate $^6C4$.
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Total Attempts: 7
Accuracy Rate: 0%
Step-by-Step Solution
The formula for combination is $^nC_r = \frac{n!}{r!(n-r)!}$. Substituting $n = 6$ and $r = 4$, we get $^6C_4 = \frac{6!}{4!(6-4)!} = \frac{6!}{4!2!} = \frac{6 \times 5 \times 4!}{4! \times 2 \times 1} = \frac{30}{2} = 15$. Therefore, option C is correct.
Detailed Options Breakdown
Option : 30
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 1: 20
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Permutations and Combinations.
Option 2: 15 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: 6
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.