Answer: (20)Cr = (20)C(20-r).
- A (20)Cr = (20)C(20-r)
- B It is not true
- C 20 is even
- D r < 10
Correct answer: A. (20)Cr = (20)C(20-r)
Explanation: Symmetry of binomial coefficients: nCr = nC(n-r). So coefficient of x<sup>r</sup> equals coefficient of x<sup>20-r</sup> in (1+x)<sup>20.</sup>
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