JEE Advanced2014MathematicsPermutation and CombinationActual
Paragraph: Box 1 contains three cards bearing numbers 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 i^ t h box, i=1,2,3 . Question: The probability that x₁, x₂, x₃ are in an arithmetic progression, is
Options
- A9 105
- B10 105
- C11 105
- D7 105
Correct answer
C. 11 105
Step-by-step solution
Here 2 x 2 = x 1 + x 3 ⇒       x 1 + x 3 = even Hence number of favorable ways =   2 C 1   .     4 C 2 +   1 C 1   .     3 C 1 = 11