Answer: 5.
- A 4
- B 3
- C 5
- D 6
Correct answer: C. 5
Explanation: nC2 = nC3: n!/(2!(n-2)!) = n!/(3!(n-3)!). Simplify: 1/2 = 1/(3(n-3)+3) ... nC2 = nC3 means (n-2)/2! = 1/3! wait: nC2 = n(n-1)/2 and nC3 = n(n-1)(n-2)/6. Set equal: 3 = n-2, n = 5.
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