Permutations And Combinations Question 118

Question: In an election the number of candidates is 1 greater than the persons to be elected. If a voter can vote in 254 ways, then the number of candidates is

Options:

A) 7

B) 10

C) 8

D) 6

Show Answer

Answer:

Correct Answer: C

Solution:

  • Let there are $ n $ candidates then $ ^{n}C_1{{+}^{n}}C_2+……{{+}^{n}}{C _{n-1}}=254 $

$ \Rightarrow $ $ 2^{n}-2=254 $

$ \Rightarrow $ $ 2^{n}=2^{8} $

$ \Rightarrow $ $ n=8 $ .