Five different written driving tests are administered by the Motor Vehicle Department. One of these five tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?

Question

ybarrap · Answer

P = P(taking a particular test) = 1/5
P(2 people take same test out of 2) = 1/5 * 1/5
P( 3 people take different tests given  first two take same test) = (4/5) * (3/5) * (2/5)
Ways that 2 people out of 5 can take the same test = 5C2 = 5!/(2!3!)
P(2 take same test and 3 take different tests) 
  = 5C2 (1/5)^2 * (4/5) *(3/5)*(2/5)
  = 48/625
  = .0768

Ans .0768