8 persons stand in a line at random. What is the probability that two persons X and Y don't stand together?

Asked by suryansudash5 | 29th Dec, 2015, 11:32: AM

Expert Answer:

8 space p e r s o n s space s tan d space i n space a space l i n e space a t space r a n d o m. T h u s space t h e y space c a n space space b e space a r r a n g e d space t h e m s e l v e s space i n space 8 factorial space w a y s. T h e r e f o r e space t h e space t o t a l space n u m b e r space o f space w a y s equals 8 factorial equals 40320  C o n s i d e r space X space a n d space Y space s tan d space t o g e t h e r. T h e n space t h e y space c a n space b e space c o n s i d e r e d space a s space o n e space u n i t. H e n c e space t h e y space f o r m space a space g r o u p space o f space 7 S o space 7 space p e o p l e space c a n space b e space a r r a n g e d space i n space 7 factorial space w a y s A l s o space X space a n d space Y space t h e m s e l v e s space c a n space b e space a r r a n g e d space i n space 2 factorial space w a y s. T h u s space t h e space n u m b e r space o f space w a y s space s u c h space t h a t space X space a n d space Y space d o n t space s tan d space t o g e t h e r equals 8 factorial minus 7 factorial cross times 2 factorial equals 30240  T h u s space t h e space p r o b a b i l i t y space t h a t space t w o space p e r s o n s space X space a n d space Y space d o n t space s t a n d space t o g e t h e r space equals 30240 over 40320 equals 0.75

Answered by Vimala Ramamurthy | 30th Dec, 2015, 11:14: AM