Question
Download Solution PDFWhat is the number of positive integer solutions of ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The number of positive integer solutions for the equation x + y + z = n is given by the combination formula:
Number of solutions = C(n - 1, k - 1), where k is the number of variables.
Formula Used:
C(n, r) = n! / [r! × (n - r)!]
Calculation:
Here, n = 5 and k = 3.
The number of solutions is:
⇒ C(5 - 1, 3 - 1) = C(4, 2)
⇒ C(4, 2) = 4! / [2! × (4 - 2)!]
⇒ C(4, 2) = 24 / [2 × 2]
⇒ C(4, 2) = 6
The correct answer is Option 3.
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