In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a
shelf so that two books on Hindi may not be together?	Options:
A) 1240	B) 1280	C) 1340	D) 1440	E) 1540
In order that two books on Hindi are never together, we must place all these books as under:   X E X E X E X .... X E X   where E - denotes the position of an English book and X that of a Hindi 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 = 22 x 21 x 20 = 1540 ways.   3 x 2 x 1   Hence, the required number of ways = 1540.   ANSW1540R:1540
<result>E</result>
In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a
shelf so that two books on Hindi may not be together?