Question

The number of ways of selecting two squares from a chess board so that they have exactly one common corner is

• A. $36$
• B. $72$
• C. $98$
• D. $112$

Answer 1

The correct option is C $98$

Now taking the only one direction of the diagonal then making two diagonally adjecent square as one group then we have to select only one group like that
above is applicable for other directional cubes as well
So total possible ways are $=2({}^7{C}_1+2({}^6{C}_1+{}^5{C}_1+{}^4{C}_1+{}^3{C}_1+{}^1{C}_1+{}^1{C}_1))=2[7+2(21\left)\right]=98$