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Question Number 115916 by I want to learn more last updated on 29/Sep/20

	Answered by mr W last updated on 30/Sep/20

	$s a y t h e f i r s t s h e l f h a s k b o o k s,$ $t h e n t h e s e c o n d s h e l f h a s 15 - k b o o k s .$ $1 ⩽ k ⩽ 14$ $t o s e l e c t k b o o k s t h e r e a r e C_{k}^{15} w a y s .$ $t o p l a c e k b o o k s t h e r e a r e k! w a y s .$ $t o p l a c e 15 - k b o o k s t h e r e a r e (15 - k)! w a y s .$ $t o t a l l y :$ $\underset{k = 1}{\sum^{14}} C_{k}^{15} k! (15 - k)!$ $= \underset{k = 1}{\sum^{14}} 15!$ $= 14 \times 15!$
	Commented by I want to learn more last updated on 30/Sep/20

	$Thanks sir, but the text answer says 14 \times 15!$
	Commented by mr W last updated on 30/Sep/20

	$i c o n s i d e r e d m y a n s w e r a g a i n .$
	Commented by I want to learn more last updated on 01/Oct/20

	$Thank you sir for your time$
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