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Easy

Question

The number of non negative integral solutions of equation 3x + y + z = 24

  1. 117    
  2. 107    
  3. 97    
  4. None of these    

The correct answer is: 117


    3x + y + z = 24, x greater or equal than 0, y greater or equal than 0, z greater or equal than 0
    Let x = k rightwards double arrow y + z = 24 – 3k …(1)
    rightwards double arrow 24 – 3k greater or equal thanrightwards double arrowless or equal than 8
    rightwards double arrow 0 less or equal thanless or equal than 8
    For fixed value of k the number of solutions of (1) is
    24–3k+2–1C2–1
    = 25–3kC1
    = 25 – 3k
    Hence number of solutions
    not stretchy sum subscript k equals 0 end subscript superscript 8 end superscript left parenthesis 25 minus 3 k right parenthesis= 25 × 9 – fraction numerator 3 cross times 8 cross times 9 over denominator 2 end fraction= 225 – 108 = 117.

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