(Q). In an election number of contestants is one more than the number of seats. If a voter can give minimum 1 and maximum equal to the number of seats vote then in how many different ways a particular voter can vote?
(i) 2044
(ii)2045
(iii) 2046
(iv) none of these
Solution:-
Let number of contestants is = n
∴ number of seats = n – 1
∴ number of ways a voter can vote is
= ⁿC₁ + ⁿC₂ + ⁿC₃ + ……………ⁿCₙ₋₁
= (ⁿC₀ + ⁿC₁ + ⁿC₂ + ⁿC₃ + ……………ⁿCₙ₋₁ + ⁿCₙ) – (ⁿC₀ +ⁿCₙ)
= 2ⁿ – 2
So total number of ways in which a voter can vote should be in 2ⁿ – 2 form, from the given options only 2046 is in this format.
Hence the Answer is (iii). 2046 Answer
