WAEC Further Mathematics 2025 Theory — Question 2

Model answer

⁸C₂=28, ⁷C₃=35 (using the general expansion x(x-1)/2! and x(x-1)(x-2)/3! forms with n=8,7). Simplifying x(x-1)/2 + x(x-1)(x-2)/6 - 4x = 0, multiplying through by 6 and factorising gives x(x²-25)=0, so x=0, 5, or -5. Since x is a positive integer, x = 5.