Asked by Epic
How many different sequences of ten flips of a coin have at least 8 heads?
Answers
Answered by
Better Than Epic
wow AoPS Counting and Probability class, the answer is 56.
Answered by
Better Than Better Than Epic
Cheating is bad, but the answer is 56. AOPS MUCH
Answered by
Anonymous
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
Answered by
Burn
Ya dont cheat
Answered by
Anonymous
Don't cheat. but if you need the answer because you are stuck, the answer is 56.
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