Ways to make the sum K is coefficient of xK in (x+x2)10 Coefficient of xK in x10(1+x)10 Coefficient of xK−10 in (1+x)10 Which is 10CK−10 So ways to make sum minimum K is 10CK−10+10CK−9+10CK−8+...+10C10 Probability
P(K)=
10CK−10+10CK−9+10C10
210
P(K)=
210−(10C0+....+10CK−11)
210
=1−
10C0+....+10CK−11
210
>
1
2
But K should be maximum so 10CK−11=10C5 (middle value) So that 10C0+....+10CK−11 is max So K = 16