Question

There are (p+q) different books on different topics in mathematics.If l=the nos of ways in which these books

Answer 1

Given :   There are (p + q) different books on different topics in Mathematics . L= The number of ways in which these books are distributed between two students X and Y such that X get p books and Y gets q books

To find :  L

Solution:

There are (p + q) different books on different topics in Mathematics, where p≠q. If L= The number of ways in which these books are distributed between two students X and Y such that X get p books and Y gets q books

Total Books = p + q  

Lets say X gets p books then

books can be Distributed in p + q  P  p   book     $^{p + q} P_{p}$

= (p + q) !/ p ! (p + q - p ) !

= (p + q) !/ p ! q !

Even if we check for Y get q  books

then

books can be Distributed in p + q  P  q  book     $^{p + q} P_{q}$

= (p + q) !/ q ! (p + q - q ) !

= (p + q) !/ q ! p !

=  (p + q) !/ p ! q !

Hence L  =  (p + q) !/ p ! q !  

Another way

p + q  books can be in (p + q) !

X can get boos in p! ways

Y can get books in q! ways

Hence number of ways =   (p + q) !/ p ! q !  

L  =  (p + q) !/ p ! q !  

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