Help with a binomial distribution problem

Question

You roll a standard die 24 times. Knowing that the event satisfies the requirements for a binomial distribution, find the probability that exactly 4 of the rolls show a 6.

Answer 1

The particular term of the binomial expansion (p+q)²⁴ representing 4 sixes rolled in the 24 'Bernoulli trials' consists of three factors:

₂₄C₄, representing # of combinations of four sixes in the 20 trials,

p⁴ representing the probability of Success (defined as rolling "6"), where p = 1/6,

q²⁰ representing the probability of Failure (rolling not a "6"), where p = 5/6.

 

To compute this term, we multiply the above three numbers, to obtain the

probability of exactly 4 "6" rolls out of 24 rolls = 0.213865, approx.