Try this beautiful Chessboard Problem based on Chessboard from PRMO - 2018.
What is the number of ways in which one can choose 60 units square from a $11 \times 11$ chessboard such that no two chosen square have a side in common?
,
Game problem
Chess board
combination
Pre College Mathematics
Prmo-2018, Problem-26
\(62\)
Total no. of squares $=121$
Out of these, 61 squares can be placed diagonally. From these any 60 can be selected in ${ }^{61} C_{60}$ ways $=61$
Now can you finish the problem?
From the remaining 60 squares 60 can be chosen in any one way
Total equal to ${ }^{61} \mathrm{C}{60}+{ }^{60} \mathrm{C}{60}=61+1=62$
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