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If x, y, z are integers and x greater or equal than 0, y greater or equal than 1, z greater or equal than 2, x + y + z = 15, then the number of values of the ordered triplet (x, y, z) is -

Maths-General

  1. 91    
  2. 455    
  3. 17C15    
  4. None of these    

    Answer:The correct answer is: 91Let y = p + 1 and z = q + 2.
    Then x greater or equal than 0, p greater or equal than 0, q greater or equal than 0 and x + y + z = 15
    rightwards double arrow x + p + q = 12
    therefore The reqd. number of values of (x, y, z) and hence of (x, p, q)
    = No. of non-negative integral solutions of x + p + q= 12
    = Coeff. of x12 in (x0 + x1 + x2 + ……)3
    = Coeff. of x12 in (1 – x)–3
    = Coeff. of x12 in [2C0 + 3C1 x + 4C2 x2 + ….]
    = 14C12 = fraction numerator 14 factorial over denominator 2 factorial 12 factorial end fraction = fraction numerator 14 cross times 13 over denominator 2 end fraction = 91.

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