Please show work Eightyone percent of all students at a cert

Please show work.

Eighty-one percent of all students at a certain school ski. If a sample of 35 students at this school is selected, and if their responses are independent, find the probability that exactly 22 of the 35 students ski All 35 students ski

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

a)
P( X = 22 ) = ( 35 22 ) * ( 0.81^22) * ( 1 - 0.81 )^13
= 0.006
b)
P( X = 35 ) = ( 35 35 ) * ( 0.81^35) * ( 1 - 0.81 )^0
= 0.0006