How many different sequences of ten flips of a coin have at least 8 heads?
5 answers
wow AoPS Counting and Probability class, the answer is 56.
Cheating is bad, but the answer is 56. AOPS MUCH
We find the number of sequences with 8 heads, 9 heads, and 10 heads
separately and add these totals. There are ${10\choose 8} = {10\choose 2} =
45$ sequences with 8 heads, ${10\choose 9} = {10\choose 1} = 10$ sequences
with 9 heads, and only 1 with 10 heads. Thus, there's a total of
$45+10+1 = 56$ sequences of ten flips with at least 8 heads
separately and add these totals. There are ${10\choose 8} = {10\choose 2} =
45$ sequences with 8 heads, ${10\choose 9} = {10\choose 1} = 10$ sequences
with 9 heads, and only 1 with 10 heads. Thus, there's a total of
$45+10+1 = 56$ sequences of ten flips with at least 8 heads
Ya dont cheat
Don't cheat. but if you need the answer because you are stuck, the answer is 56.