Number of ways of distributing n identical items among r persons such that anyone can get any number of items is : n+r-1Cr-1 .

Now,in X1 + X2 +X3 +X4 +X5 +X6 =45 We have to distribute 45 1s into six entities namely X1 ,X2..... . {1s being identical to each other}

Answer should have been : (45+6-1)C(6-1)=50C5 .

But we are given condition that X1,X2,X3>=5

Therefore 15 1s have already been distributed among X1,X2,X3 .So from remaining 30 1s we start distibuting among X1,X2..using above formula ..

30+6-1C6-1 = 35C5

Hope This helps .