UPSC NDA I 2025 Mathematics Paper

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