(Q). In an election the number of contestant is one more than the number of seats. A voter can give minimum 1 and maximum equal to the number of seats. Then find the number of contestant if a particular voter can vote in 510 different ways.
Solution:-
Let the number of contestants = n
∴ number of seats = n – 1
So a particular voter can give 1 or 2 or 3 or ……….. (n -1) votes.
∴ Number of ways a voter can vote is =
ⁿC₁ + ⁿC₂ + ⁿC₃ + …………….. + ⁿCₙ₋₁
=(ⁿC₀ + ⁿC₁ + ⁿC₂ + ⁿC₃ + …………….. + ⁿCₙ₋₁ + ⁿCₙ) – (ⁿC₀ + ⁿCₙ)
⟹ 2ⁿ – 2 = 510 (given in question)
⟹ 2ⁿ = 512
⟹ 2ⁿ = 2⁹
∴ n = 9
∴ Number of contestants = 9 Answer
