There are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.
Consider the provided information.
A coin is flipped eight times where each flip comes up either heads or tails.
Part (a) How many possible outcomes are there in total?
Each time we flip a coin it comes up either heads or tail.
Therefore the total number of ways are: 2⁸ = 256
Hence, there are 256 ways in total.
Part (b) contain exactly three heads?
We want exactly 3 heads, therefore,
n=8 and r=3
According to the definition of combination:
To get exactly 3 heads,
n=8 and r=3
(⁸C₃ ) = 8! / 3!(5!) = 56.
Therefore, there are 256 ways in total and 56 possible outcomes contain exactly three heads. The possible outcomes contain at least three heads is 219.
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