How many possible outcomes of tossing a coin 3 times have exactly 2 heads?

Answer 1

Three outcomes are possible: THH or HTH or HHT, so the probability of getting exactly 2 heads from three tosses of a fair coin is 3x0.53=0.375

In general, the number of different ways of getting k heads from n coin tosses is given by n! / ( k! x (n-k)! ), which is known as the binomial coefficient. The "!" notation is "the factorial"; for some number s, s! = s x (s-1) x (s-2) ... 2 x 1, so that 3! = 3x2x1, 5! = 5x4x3x2x1 and so on.

Thus your question can be answered by replacing n and k in the formula above, such that the number of ways is 3! / ( 2! x 1!) = 3. This is true for all experiments where you perform some experiment with two possible outcomes n times and record how many times one of the events occurs. Another typical example would be the number of times you roll a 4 after 10 rolls of a dice, and there are 10! / 6!x4! = 210 ways of doing this.