in+how+many+ways+can+you+choose+3 small+squares+on+chess+board+so+that+none+of+them+are+in+same+row,+ column+or+diagonal+line+by+combinations+and+permutations

Dear student,

In a square board there are 8 rows and 8 columns, now use the basic property of P and C

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

Total number of squares on a chessboard are 64 i.e 8*8

Number of ways we can choose 3 squares = ⁶⁴C₃

number of ways we can choose 3 squares so that they are in the same column is 8C3 * 8 * 3! =48 * 8C3

number of ways we can choose 3 squares in same row = 48 * 8C3

number of ways we can choose 3 squares in same diagonal = 8*8C3

so number of ways we can choose 3 squares so that they are not in the same row or column or diagnal is 64C3 - 48*8C3 - 48*8C3 - 8*8C3

please approve !