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Find the number of permutationn of n different things taken r at a  time such that two specific thing occur together 
Asked by neeraj.unnao | 26 Dec, 2016, 22:58: PM
answered-by-expert Expert Answer
begin mathsize 16px style F i r s t space l e t space u s space l e a v e space o u t space t w o space s p e c i f i e d space o b j e c t s. T h e n comma space t h e space n u m b e r space o f space p e r m u t a t i o n s space o f space t h e space r e m a i n i n g space left parenthesis n minus 2 right parenthesis space o b j e c t s comma space t a k e n space left parenthesis r minus 2 right parenthesis space a t space a space t i m e equals P presuperscript n minus 2 end presuperscript subscript r minus 2 end subscript N o w comma space c o n s i d e r space t w o space s p e c i f i e d space o b j e c t s space t e m p o r a r i l y space a s space a space sin g l e space o b j e c t space a n d space a d d space i t space t o space e a c h space o f space t h e s e space P presuperscript n minus 2 end presuperscript subscript r minus 2 end subscript space p e r m u t a t i o n s space w h i c h space c a n space b e space d o n e space i n space left parenthesis r minus 1 right parenthesis space w a y s. T h u s comma space t h e space n u m b e r space o f space p e r m u t a t i o n s space b e c o m e s space left parenthesis r minus 1 right parenthesis P presuperscript n minus 2 end presuperscript subscript r minus 2 end subscript B u t space t w o space s p e c i f i e d space t h i n g s space c a n space b e space p u t space t o g e t h e r space i n space 2 factorial space w a y s. H e n c e comma space r e q u i r e d space n u m b e r space o f space p e r m u t a t i o n s equals 2 factorial space left parenthesis r minus 1 right parenthesis P presuperscript n minus 2 end presuperscript subscript r minus 2 end subscript end style
Answered by Rashmi Khot | 27 Dec, 2016, 09:07: AM
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