The president of a republic wishes to assign the premiership,the vice-premiership,and six other cabinet posts to a selected group of 8,comprising of 6 career diplomats and 2 business men.If none of the business men can be made premier or vice premier,in how many ways can the 8 posts be assigned to the 8 people?


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Question Number 27514 by NECx last updated on 08/Jan/18

$T h e p r e s i d e n t o f a r e p u b l i c w i s h e s$ $t o a s s i g n t h e p r e m i e r s h i p, t h e$ $v i c e - p r e m i e r s h i p, a n d s i x o t h e r$ $c a b i n e t p o s t s t o a s e l e c t e d g r o u p$ $o f 8, c o m p r i s i n g o f 6 c a r e e r$ $d i p l o m a t s a n d 2 b u s i n e s s m e n . I f$ $n o n e o f t h e b u s i n e s s m e n c a n b e$ $m a d e p r e m i e r o r v i c e p r e m i e r, i n$ $h o w m a n y w a y s c a n t h e 8 p o s t s$ $b e a s s i g n e d t o t h e 8 p e o p l e ?$
	Answered by Rasheed.Sindhi last updated on 08/Jan/18

	$The upper 2 posts can be selected$ $from only 6 diplomats$ $Hence they can be selected$ $in 6 \times 5 = 30 ways (One can be$ $selected in 6 ways and after that$ $the other can be selected from$ $5 remaining diplomates)$ $After the above selection there$ $remains 6 persons (4 diplomates$ $and 2 business men) and 6 posts$ $so they can be filled 6! ways .$ $∴ Toal ways = (6.5) (6!) = 21600$
	Commented by NECx last updated on 29/Apr/18

	$T h a n k y o u s o m u c h s i r .$
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