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The total number of positive integral solution for x, y, z such that xyz = 24, is

       (a) 30    ,  (b) 60 ,    (c) 90  , (d) 120

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The correct answer is option  a)30 

solution:::

xyz = 24

xyz = 23 × 31

The number of ways of distributing 'n' identical balls into 'r' different boxes is (r − 1)C(r − 1)

Here we have to group 4 numbers into three groups

Number of integral positive solutions

(3 + 3 − 1)C(3 − 1) × (1+ 3 − 1)C(3 − 1)

5C2 × 3C2 = 30

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