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JEE Main & Advanced JEE Main Paper (Held On 12-Jan-2019 Morning)

  • question_answer
    Consider three boxes, each containing 10 balls labelled 1, 2, ..... 10. Suppose one ball is randomly drawn from each of the boxes. Denote by \[{{n}_{i}},\]the label of the ball drawn from the \[{{i}^{th}}\] box, (i = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that \[{{n}_{1}}<{{n}_{2}}<{{n}_{3}}\] is [JEE Main Online Paper Held On 12-Jan-2019 Morning]

    A) 120                              

    B) 164  

    C) 240                  

    D)   82

    Correct Answer: A

    Solution :

    Let \[{{n}_{1}}=1,\]then \[{{n}_{2}}\]can be 2, 3,..., 9 and \[{{n}_{3}}\]can be 3,...., 10 \[\therefore \] No. of ways \[=8+7+6+5+4+3+2+1\]\[=\frac{8\times 9}{2}\] Similarly, when \[{{n}_{1}}=2,\]then \[{{n}_{2}}\] can be 3,..., 9 and \[{{n}_{3}}\] can be 4,...., 10 \[\therefore \]No. of ways\[=7+6+5+4+3+2+1=\frac{7\times 8}{2}\] And so on. \[\therefore \]Total required ways \[=\frac{8\times 9}{2}+\frac{7\times 8}{2}+....+\frac{2\times 3}{2}+\frac{1\times 2}{2}=\frac{240}{2}=120\]


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