There are 24 teams participating in a math competition from 8 different school, one team per class. The competition is from 8 to 10th class. Find the probability of  
a) Coming 1st from each class per school.
b) Getting a prize if there are three prizes per class, 1,2,3.

Asked by Balbir | 14th Dec, 2015, 09:13: PM

Expert Answer:

G i v e n space t h a t space t h e r e space a r e space 24 space t e a m s space f r o m space 8 space d i f f e r e n t space s c h o o l s. T h u s comma space t h e space n u m b e r space t e a m s space p e r space s c h o o l equals 24 over 8 equals 3 A l s o space g i v e n space t h a t space t h e r e space i s space o n e space t e a m space p e r space c l a s s space i n space t h e space c o m p e t i t i o n. T h e r e f o r e comma space t h e r e space a r e space 3 space c l a s s e s space f r o m space e a c h space s c h o o l. left parenthesis a right parenthesis L e t space A space b e space t h e space e v e n t space f o r space c o m i n g space f i r s t space f r o m space e a c h space c l a s s space p e r space s c h o o l. T h e r e space a r e space 8 space s c h o o l s. S u p p o s e space a space t e a m space i s space c o m i n g space f i r s t space i n space t h e space c o m p e t i t i o n. T h u s comma space t h e space p r o b a b i l i t y space o f space c o m i n g space f i r s t space f o r space o n e space c l a s s equals 1 over 8 N o w space t h e r e space a r e space s e v e n space s c h o o l s. T h u s comma space t h e space p r o b a b i l t y space o f space c o m i n g space f i r s t space i n space t h e space c o m p e t i t i o n space f o r space a n o t h e r space c l a s s equals 1 over 7 N o w space t h e r e space a r e space s i x space s c h o o l s. T h u s comma space t h e space p r o b a b i l t y space o f space c o m i n g space f i r s t space i n space t h e space c o m p e t i t i o n space f o r space a n o t h e r space c l a s s equals 1 over 6 T h e r e f o r e comma space t h e space p r o b a b i l i t y space o f space c o m i n g space f i r s t space f r o m space e a c h space c l a s s space p e r space s c h o o l equals 1 over 8 cross times 1 over 7 cross times 1 over 6 equals 1 over 336 left parenthesis b right parenthesis T h e r e space a r e space 3 space p r i z e s space p e r space c l a s s space a n d space t h e r e space a r e space 8 space s c h o o l s. T h u s space t h e space p r o b a b i l i t y space o f space g e t t i n g space t h r e e space p r i z e s space f o r space o n e space c l a s s equals 3 over 8 A n d space space t h e space p r o b a b i l i t y space o f space g e t t i n g space t h r e e space p r i z e s space f o r space a n o t h e r space c l a s s equals 3 over 8 A l s o space t h e space p r o b a b i l i t y space o f space g e t t i n g space t h r e e space p r i z e s space f o r space o n e space m o r e space c l a s s equals 3 over 8 T h u s comma space t h e space p r o b a b i l i t y space o f space g e t t i n g space t h r e e space p r i z e s space p e r space c l a s s equals 3 over 8 cross times 3 over 8 cross times 3 over 8 equals 27 over 512

Answered by Vimala Ramamurthy | 15th Dec, 2015, 11:04: AM