JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Self Evaluation Test - Permutations and Combinatioins

  • question_answer
    Find the number of integral solution of the equation \[x+y+z=20\] and \[x>-1,y>-2\] and \[z>-3.\]

    A) \[^{25}{{C}_{23}}\]

    B) \[^{17}{{C}_{2}}\]

    C) \[^{23}{{C}_{2}}\]     

    D) None of these

    Correct Answer: A

    Solution :

    [a] Since as per the given condition \[x>-1,\] so x is non-negative integer, \[y>-2\,\,so\,\,y=-1+b\] and similarly \[z>3\,\,so\,\,z=-2+c\] or \[(x)+(-1+b)+(-2+c)=23\] or \[x+b+c=23\] And we need to find the number of non-negative integral solution of the equation \[x+b+c=23\] which is,  \[^{23+3-1}{{C}_{3-1}}{{=}^{25}}{{C}_{2}}{{=}^{25}}{{C}_{23}}\]

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