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


1. 30
2. 24
3. 48
4. 60

1 Answer

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Correct Answer - Option 1 : 30

Calculation:

We have,

⇒ 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

⇒ The total number of ways in which n identical items can be distributed among p persons so that each person may get any number of items is n+p-1Cp-1.

⇒ Total number of ways in which n identical items can be distributed among p persons such that each of them receive at least one item n-1Cp-1

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