In how many ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?  Choose the correct choice from the following options:
A) 4586
B) 5896
C) 2415
D) 1771
E) 1881

Rationale: "in order that two books on hindi are never together , we must place all these books as under : h e h e h e h … . . h e h where h denotes the position of hindi book and e that of english book . since there are 22 books on english , the number of places marked e are 23 . now , 20 places out of 23 can be chosen in 23 c 20 = 23 c 3 = 23 * 22 * 21 3 * 2 * 1 = 1771 ways . hence the number of ways = 1771 ways answer : d"
Answer: D