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 ? Options:	A) 3990	B) 1540	C) 1995	D) 3672	E) None of these
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 22C19 = 22C3 = (22x21x20)/(3x2x1) = 1540 ways   Answer 1540.
<result>B</result>
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 ?