Five persons entered the lift cabin in the ground floor of an 8-floor house.Suppose each of them can leave the cabin independently at any floor beginning with the first. Find the total number of ways in which each of the five persons can leave the cabin (i)at any one of the 7 floors (ii)at different floors.

Asked by Alekhya K | 3rd Oct, 2014, 06:46: PM

Expert Answer:

left parenthesis i right parenthesis S u p p o s e space t h e r e space a r e space f i v e space p e r s o n s. T h e space f i r s t space p e r s o n space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 7 space d i f f e r e n t space w a y s. T h e space s e c o n d space p e r s o n space space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 7 space d i f f e r e n t space w a y s. T h e space t h i r d space p e r s o n space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 7 space d i f f e r e n t space w a y s. T h e space f o u r t h space p e r s o n space space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 7 space d i f f e r e n t space w a y s. T h e space f i f t h space p e r s o n space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 7 space d i f f e r e n t space w a y s. T h u s comma space b y space p r o d u c t space r u l e comma 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 comma space i n space w h i c h space e a c h space o f space t h e space f i v e space p e r s o n s c a n space l e a v e space t h e space l i f t space c a b i n space a t space a n y space o n e space o f space t h e space f l o o r s equals 7 cross times 7 cross times 7 cross times 7 cross times 7 equals 7 to the power of 5 equals 16807 left parenthesis i right parenthesis S u p p o s e space t h e r e space a r e space f i v e space p e r s o n s. T h e space f i r s t space p e r s o n space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 7 space d i f f e r e n t space w a y s. T h e space s e c o n d space p e r s o n space space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 6 space d i f f e r e n t space w a y s. T h e space t h i r d space p e r s o n space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 5 space d i f f e r e n t space w a y s. T h e space f o u r t h space p e r s o n space space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 4 space d i f f e r e n t space w a y s. T h e space f i f t h space p e r s o n space c a n space l e a v e space t h e space l i f t space c a b i n space i n space 3 space d i f f e r e n t space w a y s. T h u s comma space b y space p r o d u c t space r u l e comma 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 comma space i n space w h i c h space e a c h space o f space t h e space f i v e space p e r s o n s c a n space l e a v e space t h e space l i f t space c a b i n space a t space d i f f e r e n t space f l o o r s equals 7 cross times 6 cross times 5 cross times 4 cross times 3 equals 2520

Answered by Vimala Ramamurthy | 4th Oct, 2014, 12:20: PM

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