We have,x+y+z+t=10....(i) Whenx≥2,z≥5 let‌‌x′=x−2 ⇒‌‌x=x′+2 z′=z−5 ⇒‌‌z=z′+5 Here,x′,z′,y≥0andt≥0are non-negative integers. ∴Substitude these value in Eq. (i), we get ‌(x′+2)+y+(z′+5)+t=10 ⇒‌‌x′+y+z′+t=3...(ii) ∴ Number of non-negative integral solution for Eq. (ii) ‌=‌3+4−1C4−1=‌6C3 ‌=‌