Nine chairs in a row are to be occupied by six students and Prof George , Prof Pieter, and Prof John. These three professors arrive before the six students and decide to choose their chairs so that each professor will be between two students. In how many ways can Professor George , Pieter and John choose their chairs ?


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Question Number 123878 by liberty last updated on 29/Nov/20

$N i n e c h a i r s i n a r o w a r e t o b e o c c u p i e d b y$ $s i x s t u d e n t s a n d P r o f G e o r g e, P r o f P i e t e r,$ $a n d P r o f J o h n . T h e s e t h r e e p r o f e s s o r s a r r i v e$ $b e f o r e t h e s i x s t u d e n t s a n d d e c i d e t o c h o o s e$ $t h e i r c h a i r s s o t h a t e a c h p r o f e s s o r w i l l b e b e t w e e n$ $t w o s t u d e n t s . I n h o w m a n y w a y s c a n P r o f e s s o r G e o r g e$ $, P i e t e r a n d J o h n c h o o s e t h e i r c h a i r s ?$
	Answered by john_santu last updated on 29/Nov/20

	$l e t \oplus = p l a c e f o r 3 p r o f e s s o r$ $△ = p l a c e f o r s t u d e n t$ $△ △ \oplus △ △ \oplus △ △ \oplus △ △ \oplus △ △ \oplus$ $= P_{3}^{5} = \frac{5!}{2!} = 60 w a y s$
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