How do I solve this Consider an experiment involving drawing

How do I solve this?

Consider an experiment involving drawing n = 30 balls from an urn which contains 800 white balls and 200 black balls. What is (approximately) the probability that less than 6 balls are black ? 0.4460 0.3290 0.3840 0.3908 0.6060

Solution

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

p = Picking a balck ball from the urn = 200/1000 = 0.20
P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)   
= ( 30 5 ) * 0.2^5 * ( 1- 0.2 ) ^25 + ( 30 4 ) * 0.2^4 * ( 1- 0.2 ) ^26 + ( 30 3 ) * 0.2^3 * ( 1- 0.2 ) ^27 + ( 30 2 ) * 0.2^2 * ( 1- 0.2 ) ^28 + ( 30 1 ) * 0.2^1 * ( 1- 0.2 ) ^29 + ( 30 0 ) * 0.2^0 * ( 1- 0.2 ) ^30
= 0.4275