Seven different written driving tests are administered by th

Seven different written driving tests are administered by the Motor Vehicle Department. One of these 7 tests is selected at random for each applicant for a driver\'s license.If a group consisting of two women and three men apply for a license, what is the probability that exactly two of the five will take the same test?

Solution

qa
the 2 who take the same test can be any of 5c2 = 10 pairs
the 1st can take any of 5 tests , the other has to take the same test
& the remaining 3 all have to take different tests, so
Pr = 10* 1/5 *4/5 * 3/5 * 2/5 = 48/125 <--------
= 0.384
qb
1st women can take any test, 2nd has to take the same test,
others may take any test, so
Pr = 1/5 <-------

= 0.2