A coin is tossed 12 times. How many different sequences of tosses could there have been, if the number of heads was at least 10?
Difficult question! I will be here waiting for an answer. Flappy Bird
There are two possible outcomes of a coin toss: heads (H) or tails (T).
For the number of heads to be at least 10 in 12 tosses, there must be either 10, 11 or 12 heads.
If there were 12 heads, there would only be 1 possible sequence: HHHHHHHHHHHH.
If there were 11 heads, there are 12 possible sequences: THHHHHHHHHHH, HTHHHHHHHHHH, and so on.
If there were 10 heads, there are 96 possible sequences.
So, the total number of possible sequences with at least 10 heads is 1 + 12 + 96 = 109.