Answer: 10C4.
- A 10C4
- B 10C2 = 45
- C 120
- D 252
Correct answer: A. 10C4
Explanation: T(r+1) = 10Cr (x2)10-r (x-3)r = 10Cr x20-2r-3r = 10Cr x20-5r. For independent term: 20-5r=0, r=4. T5 = 10C4 = 210.
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