Mathematics · Permutations, Combinations, and Binomial Theorem
Which of the following statements regarding Permutations, Combinations, and the Binomial Theorem are CORRECT? I. The sum of combinations nCr and nCr - 1 is equal to n + 1Cr, which is known as Pascal's Identity. II. The number of circular permutations of n distinct objects where clockwise and anticlockwise arrangements are considered identical is given by (n - 1)!2. III. The alternating sum of binomial coefficients evaluates to zero. IV. The sum of all even combinations (nC0 + nC2 + nC4 + ...) is equal to 2n - 1. Choose the most appropriate answer from the options given below:
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1I, II and IV Only
- 2II, III and IV Only
- 3I, III and IV Only✓
- 4I, II and III Only
Correct answer
I, III and IV Only
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