Four people toss a fair coin and the odd one out pays for coffee. If the coins all turn up the same or show two heads and two tails, they toss again. (a) Find the probability that the 'odd person' is picked in one round of tosses. (b) Let X be the number of rounds of tosses until the 'odd person' being found. Find the probability mass function (pmf) of X? Find E(X), the expected number of rounds needed. (c) Find the cumulative distribution function (CDF) of X. Find the probability that at least 5 rounds of tosses are needed.

I need an explanation for part (a) as to why its 4C3 and 4C1 when the odds of selecting one 'odd person' is the same.