how do i know when to use permutation or combination

Asked by Saksham | 14th Sep, 2015, 10:26: PM

Expert Answer:

P e r m u t a t i o n colon W h e n space s e l e c t i o n space a n d space a r r a n g e m e n t space o f space t h i n g s space i n space a space d e f i n i t e space o r d e r space a r e space c o n s i d e r e d comma space t h e n space P e r m u t a t i o n space i s space u s e d. E x a m p l e colon I n space h o w space m a n y space w a y s space 7 space w i n d o w s space c a n space b e space p a i n t e d space f r o m space 4 space d i f f e r e n t space c o l o u r s space o f space p a i n t ? S o l u t i o n colon T h e space n u m b e r space o f space w a y s space i n space w h i c h space 7 space w i n d o w s space c a n space b e space p a i n t e d space f r o m space 4 space c o l o u r s space o f space p a i n t space i s space s a m e a s space t h e space n u m b e r space o f space a r r a n g e m e n t space o f space 7 space t h i n g s comma space t a k i n g space 4 space a t space a space t i m e. H e n c e space t h e space r e q u i r e d space n u m b e r equals P presuperscript 7 subscript 4 equals fraction numerator 7 factorial over denominator open parentheses 7 minus 4 close parentheses factorial end fraction equals 210 C o m b i n a t i o n colon W h e n space s e l e c t i o n s space a r e space m a d e space b y space t a k i n g space s o m e space o r space a l l space o f space t h e space t h i n g s comma space i r r e s p e c t i v e space o f space t h e i r space a r r a n g e m e n t s t h e n space C o m b i n a t i o n space i s space u s e d. E x a m p l e colon I f space t h e r e space a r e space 25 space p e r s o n s space i n space a space p a r t y comma space a n d space e a c h space o n e space p e r s o n space s h a k e space h a n d s space w i t h space e v e r y space o t h e r p e r s o n comma space t h e n space i n space h o w space m a n y space h a n d space s h a k e s space h a p p e n space i n space t h e space p a r t y ? S o l u t i o n colon W h e n space t w o space p e r s o n s space s h a k e space h a n d s comma space i t space i s space c o u n t e d space a s space o n e space h a n d s h a k e. H e r e comma space t h e space o r d e r space i s space n o t space i m p o r tan t. H e n c e space i t space i s space a space c o m b i n a t i o n. T h e space t o t a l space n u m b e r space o f space h a n d s h a k e s space i s space s a m e space a s space t h e space n u m b e r space o f space w a y s space o f space s s e l e c t i n g space 2 space p e r s o n s space a m o n g space 25 space p e r s o n s. H e n c e space t h e space r e q u i r e d space n u m b e r equals C presuperscript 25 subscript 2 equals fraction numerator 25 factorial over denominator 2 factorial open parentheses 25 minus 2 close parentheses factorial end fraction equals 300

Answered by Vimala Ramamurthy | 15th Sep, 2015, 10:25: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.