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Box 1 contains three cards bearing number 1,2,3 , box 2 contains five cards bearing numbers 1,2,3,4,5 and box 3 contains seven cards bearing numbers 1,2,3,4,5,6,7. A card is drawn from each of the boxes. Let `x_i` be the number on the card drawn from the ith box , `i=1,2,3`.
The probability that `x_1,x_2 and x_3` are in arithmetic progression , is

A

`29/105`

B

`53/105`

C

`57/105`

D

`1/2`

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