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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?

,

- \(56\)
- \(58\)
- \(60\)
- \(62\)
- \(64\)

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 ${ }^{61} \mathrm{C}{60}+{ }^{60} \mathrm{C}{60}=61+1=62$

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?

,

- \(56\)
- \(58\)
- \(60\)
- \(62\)
- \(64\)

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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