Question

In an examination of 9 papers a candidate has to pass in more papers than the number of papers in which he fails in order to be successful. The number of ways in which he can be unsuccessful is

• A. 255
• B. 256
• C. 193
• D. 319

Answer 1

Answer: (B)

256

Answer 2

The candidate is unsuccessful if he fails in 9 or 8 or 7 or 6 or 5 papers.

∴ The number of ways to be unsuccessful

= ⁹C₉ + ⁹C₈ + ⁹C₇ + ⁹C₆ + ⁹C₅ = ⁹C₀ + ⁹C₁ + ⁹C₂ + ⁹C₃ + ⁹C₄

= $\frac{1}{2}$ (⁹C₀ + ⁹C₁ + ..... + ⁹C₉) = 2⁸