AMC10 2027 - Self-practice Set 6 Question 13

Question 13

Eight people sit around a circular table and independently flip fair coins. Those with heads stand and those with tails remain seated. What is the probability that no two adjacent people stand?

$\frac{47}{256}$
$\frac3{16}$
$\frac{49}{256}$
$\frac{25}{128}$
$\frac{51}{256}$