‌x+y+z=15 ‌‌ Total no. solution ‌=‌15+3−1C3=136...‌ (1) ‌ ‌‌ Let ‌x=y≠z ‌2x+z=15⇒z=15−2t ‌⇒r∈{0,1,2,...7}−{5} ‌∴7‌ solutions ‌ ‌∴‌ there are ‌21‌ solutions in which exactly ‌ ‌‌ Two of ‌x,y,z‌ are equal ... (2) ‌ ‌‌ There is one solution in which ‌x=y=z...‌ (3) ‌ ‌‌ Required answer ‌=136−21−1=144