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You choose three numbers from 1, 2, 3, .., 21.  Find the probability that they are in arithmetic progression.

 Feb 1, 2021
 #1
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No. of sets  where common difference  (cd)  = 1   =   19

No. of sets where cd  = 2   =     17

No. of sets  where cd  =  3  =     15

No.of sets  where cd  = 4    =     13

No. of sets  where cd  =  5 =      11

No. of sets where cd =  6   =        9

No. of sets where cd  =  7    =      7

No. of sets  where cd  =  8    =     5

No. of sets  where cd  =  9    =     3

No. of sets  where cd  =  10 =      1

 

Total  sets =  =  (n sets)^2   =    (10)^2    =  100

 

C (21,3)  =  1330

 

Probability =  100 /  1330      =      10 / 133   

 

 

cool cool cool

 Feb 1, 2021
edited by CPhill  Feb 1, 2021

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