The International Olympics Committee only allows six athlete

The International Olympics Committee only allows six athletes from each country to enter the pogo-stick jumping contest. If there are 40 American athletes going to the pogo-stick jumping trials and 6 are from Tennessee, assuming equal selection what is the probability all will be Tennesseeans?

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( X = 6 ) = ( 6 6 ) * ( 0.15^6) * ( 1 - 0.15 )^0
= 0.00001139