The number of integral solution of this equation x+y+z+w<25 such that x>−2,y>1,z≥0 w>3 is

x+y+z+w<25 let  x+y+z+w+a=25  such that a>0-----1x=−1+t1    ∴    t1≥0y=2+t2    ∴    t2≥0z=t3    ∴    t3≥0w=4+t4    ∴    t4≥0a=1+t5    ∴    t5≥0 put in equation (i) −1+t1+2+t2+t3+4+t4+1+t5=25t1+t2+t3+t4+t5=19number of non negative solutions =Cr-1   n+r-1=C4   23=8855