Question: The number of ways in which we can choose 3 squares on a chess board such that one of the squares ha...

Question

The number of ways in which we can choose 3 squares on a chess board such that one of the squares has its two sides common to other two squares –

Answer 1

Either we have to choose

(i) Every square of (2 by 2)

will contribute four

Shaped figures by removing any one square out of it Number of ways to choose these squares = 7 × 7 = 49.

So, total

Shaped figures = 49 × 4 = 196.

(ii) In every line it is possible to have 6 shaped figures.

So total number of such figures = 6 × 8 × 2 = 96.

\ Total number of cases = 196 + 96 = 292.

Hence (2) is correct answer.