Question

Eight different versions of the written driving test are administrated by the Department. of Motor Vehicles. One of these eight versions is chosen at random for each applicant. If four friends apply for licenses, what is the probability that two different versions will be used twice each (i.e. two of the friends will write one version and the other two friends will write a second version)?

Answer 1

Pg for o Answert Eight different versions of the written driving test are administrated by the department of motor vehicles. there, each of the friend has 8 option thus total waya : Total no. of ways writting the test . Then, One of these eight versions is chosen at random for each applicant. The probability that two different versions will be wed twice each i firstly we will consider the no. of poirs pouible. Thus, are kind no. of pairs with friend i. let, the friends be named fi,f2, F3, FA. . 1. i can pair with either of fa, fs and fa. ie total number of ways of forming pairs = 3. o one pair selects one of the 8 versions and other pair choses from remaining 7 versions. Thus, total number of ways = 3x8x7. Hence, P(two different versions will be wed tuce each) = 3x8x7 Now,