In this task, you need to provide the correct option for a given problem on probability from the provided options.

Problem: there are 10 books on a shelf , of which 4 are paperbacks and 6 are hardbacks . how many possible selections of 5 books from the shelf contain at least one paperback and at least one hardback ? 
Options: a ) 75 , b ) 120 , c ) 210 , d ) 246 , e ) 252
d

Problem: the membership of a committee consists of 4 english teachers , 2 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be english teachers ? 
Options: a ) 2 / 3 , b ) 1 / 3 , c ) 2 / 9 , d ) 1 / 12 , e ) 3 / 28
e

Problem: how many different ways can 2 students be seated in a row of 6 desks , so that there is always at least one empty desk between the students ? 
Options: a ) 2 , b ) 3 , c ) 4 , d ) 20 , e ) 12

d