Question

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

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

Answer 1

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 ^{(n + 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