A company is taking a survey to find out whether people like its product. Its last survey indicated that $20\%$ of the population like the product. Based on that in a sample of $5$ people, find the probabilities of the following:

$($a$)$ Exactly $4$ people like the product ;

The probability is :

$($b$)$ Exactly two people likes the product;

The probability is :

$($c$)$ At least one person likes the product;

The probability is :