Question

If 8 squares are selected at random on a chessboard having 8x8 squares the probability that they will be in a diagonal line is

• A. $\frac{{}^8{C}_8}{{}^{64}{C}_8}$
• B. $\frac{2{\times }^8{C}_8}{{}^{64}{C}_8}$
• C. $\frac{4{\times }^8{C}_8}{{}^{64}{C}_8}$
• D. $\frac{6{\times }^8{C}_8}{{}^{64}{C}_8}$

Answer 1

The correct option is B $\frac{2{\times }^8{C}_8}{{}^{64}{C}_8}$

There are only 2 ways of selecting 8 squares in a diagonal line from a chessboard.
Selection of 8 squares from 8 squares in a diagonal ${=}^8{C}_8$
Probability $=\frac{2{\times }^8{C}_8}{{}^{64}{C}_8}$