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