Find the number of ways in which two squares can be selected from an 8 by 8 chess board of size 1- 1 so that they are not in the same row and in the same column-

First square can be choosen in ^64C_1 ways = 64 waysNow, 15 squares in same row amp; column cannot be choosen.Next square may be choosen in ^49C_1 ...

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Standard XII

Mathematics

Fundamental Principle of Counting

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Question

Find the number of ways in which two squares can be selected from an $8$ by $8$ chess board of size $1 \times 1$ so that they are not in the same row and in the same column.

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Solution

First square can be choosen in $^{64} C_{1}$ ways = 64 ways

Now, 15 squares in same row & column cannot be choosen.

Next square may be choosen in $^{49} C_{1} = 49$ Ways

As choice is unordered, therefore, total no of ways = $\frac{64 \times 49}{2}$

$= 1568$

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Find the number of ways in which two squares can be selected from an 8 by 8 chess board of size 1×1 so that they are not in the same row and in the same column.

First square can be choosen in 64C1 ways = 64 waysNow, 15 squares in same row & column cannot be choosen.Next square may be choosen in 49C1=49 WaysAs choice is unordered, therefore, total no of ways = 64×492=1568

Find the number of ways in which two squares can be selected from an $8$ by $8$ chess board of size $1 \times 1$ so that they are not in the same row and in the same column.

First square can be choosen in $^{64} C_{1}$ ways = 64 ways

Now, 15 squares in same row & column cannot be choosen.

Next square may be choosen in $^{49} C_{1} = 49$ Ways

As choice is unordered, therefore, total no of ways = $\frac{64 \times 49}{2}$

$= 1568$