At an annual board meeting company X is deciding whether or not to take the company public.

Question

Each board member can vote "yes", "no", or "abstain". If there are n-board members, then how many different ways can the votes be cast? Express your answer as a recursive function, f(n). Don't forget to include any necessary base cases(s).

Answer 1

Since each member can vote 1 of 3 ways ('yes', 'no', and 'abstain'), then the number of possibilities for n members is 3 * the number of (n - 1) members. (I.e. each member contributes 3x possibilities.) So, expressed as a (C) recursive function:

int f(int n) {

if (n <= 0) {

return 1;

}

return 3 * f(n - 1);

}