Question

The total numbers of integral solutions for (x,y,z) such that xyz = 24 is

• A. 36
• B. 90
• C. 96
• D. 120

Answer 1

Answer: (D)

120

Answer 2

24 can be broken as (1, 1, 24), (1, 2, 12),

(1, 3, 8) (1, 4, 6) (2, 3, 4) & (2, 2, 6)

All sets in which each no. is diff = ³C₂. 3! + 3! = 24

in which two nos. are same = ³C₂ $\frac{3 ⥂ !}{2!} + \frac{3!}{2!}$ = 12

total no. of possible sets

= 24 × 4 + 12 × 2 = 120