Answer: (n-1)Cr.
- A (n-1)Cr
- B (n-1)C(r+1)
- C nC(r-1)
- D (n+1)Cr
Correct answer: A. (n-1)Cr
Explanation: Pascal identity: nCr = (n-1)C(r-1) + (n-1)Cr. Each entry is sum of two entries directly above in Pascal triangle.
Row n of Pascal's triangle gives the coefficients nC0, nC1, ..., nCn for the expansion of (a+b)ⁿ; each number is the sum of the two numbers diagonally above it, a direct visual proof of the identity nCr = (n-1)C(r-1) + (n-1)Cr.
Concept context
Expansion of (a+b) n , general term, middle term, binomial coefficients, and greatest term