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Question Number 189716 by Mastermind last updated on 20/Mar/23

	Answered by mr W last updated on 21/Mar/23

	$5! \times 2! = 240$
	Commented by Mastermind last updated on 21/Mar/23

	$Someone said its 48$
	Commented by mr W last updated on 21/Mar/23

	$w h a t d o y o u s a y ?$
	Commented by mr W last updated on 21/Mar/23

	$m e t h o d 1 :$ $a t f i r s t o n l y t h e 5 p e o p l e o f t h e f r i e n d$ $f a m i l y w i l l b e s e a t e d . t h e r e a r e 4!$ $w a y s t o d o t h i s . b e t w e e m t h e r e a r e$ $5 p l a c e s w h e r e p e t e r a n d h i s w i f e$ $c a n b e s e a t e d . p e t e r a n d h i s w i f e c a n$ $c h a n g e t h e i r s e a t s, t h e r e a r e 2 w a y s .$ $s o t o t a l l y t h e r e a r e$ $4! \times 5 \times 2 = 240 w a y s .$ $m e t h o d 2 :$ $a t f i r s t o n l y p e t e r a n d t h e 5 p e o p l e$ $f r o m t h e f r i e n d f a m i l y w i l l b e s e a t e d .$ $t o a r r a n g e t h e 6 p e o p l e a t t h e t a b l e$ $t h e r e a r e 5! w a y s . n o w {p e t e r}^{'} s w i f e$ $t a k e s a s e a t n e x t t o p e t e r, r i g h t t o$ $h i m o r l e f t t o h i m, s o 2 w a y s .$ $t o t a l l y 5! \times 2 = 240 w a y s .$
	Answered by manolex last updated on 21/Mar/23

	$P_{c} = (n - 1)!$ $P e t e r a n d w i f e 1 2!$ $a n f i t r i o n a n d w i f e 1 e s t a b l i s h e d s i t e s 1!$ $3 f a m i l y 3$ $n = 5$ $P_{c} = 4! 2!$ $P_{c} = 48$
	Commented by mr W last updated on 21/Mar/23

	$d o p e t e r a n d h i s w i f e b e l o n g t o t h e$ $f a m i l y w h i c h i n v i t e d t h e m ? w h e n$ ${i t}^{'} s a f a m i l y o f 5 m e m b e r s, h o w$ $m a n y p e o p l e t o t a l l y a r e t a k i n g t h e$ $d i n n e r ?$ $A) 5 B) 7 C) n o n e o f b o t h$
	Commented by manolex last updated on 21/Mar/23


	Commented by manolex last updated on 21/Mar/23

	Answered by mehdee42 last updated on 21/Mar/23

	$c a s e 1) i f t h a y a r e i n a r o w \Rightarrow 6! \times 2!$ $c a s e 2) i f t h e y a r e a r o u n d a t s b l e \Rightarrow 5! \times 2!$
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