In how many ways can 21 books on English and 19 books on French be placed in a row on a shelf so that two books on French May not be Together ?
Choose the correct choice from the following
A) 3990 B) 1540 C) 1995 D) 3672 E) none of these

Rationale: "in order that two books on french are never together , we must place all books as under x e x e x e x e x e . . . . . x e x where e denotes the position of an english book and x that of a french book . since there are 21 books on english , the number of places marked x are therefore , 22 . now , 19 places out of 22 can be chosen in 22 c 19 = 22 c 3 = ( 22 x 21 x 20 ) / ( 3 x 2 x 1 ) = 1540 ways answer b ."
Answer: B