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