A coin is flipped 8 times. find the probability of the event: exactly 3 heads

H, T = 2, Flipped 8 times, Sample space = 2⁸

Exactly three heads = 3.

n = 8, r = 3 Probability of success p = (1/2), Probability of failure = (1/2)

By Binomial Probability distribution

= ⁿCr * p^r*q^ (n - r)

⁸C₃ * (1/2) ³ * (1/2) ⁸ ⁻ ³

= ⁸C₃ * (1/2) ³ * (1/2) ⁵ ⁸C ₃ = 8*7*6 / (3*2*1) = 56

= 56 * (1/8) * (1/32)

= 56/256

Probability = 56/256