JEST 2019 Descriptive Q3 (8 Marks)

Question

Determine the number of functions  f:{1,2,3…,n}→{1995,1996} satisfying the condition that  f(1)+f(2)+…f(n)  is odd.

Comments

$2^{n-1}+1$

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Can you please explain?

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for each of the n-1 elements : we have two choices $(2015$ or $2016)$=$2^{n-1}$

after this the sum of  $s=f(1)+f(2)...f(n-1)$ is either even or odd

so for the sum  $f(1)+f(2)...f(n-1)+ f(n)$ to be even we have only one choice ( when  $s$ is even-> f(n) is odd(2015) and when  s is odd-> f(n) is even(2016) ) = $2^{n-1}$