Question

The probability that a rectangle picked up from a chessboard has the area 6cm² where the distance between consecutive parallel lines on the board is 1 cm, is

(A) \(\frac 3{56}\)

(B) \(\frac 3{28}\)

(C) \(\frac 9{56}\)

(D) \(\frac {11}{108}\)

Answer 1

Correct option is (D) \(\frac{11}{108}\)

Rectangle of dimension (1 x 6) = ⁸C₁ x ^(8-6+1)C₁ = 24

Rectangle of dimension (2 x 3) = ^(8-2+1)C₁ ^(8-3+1)C₁ = 42

Total number of rectangle of 6 cm =  2 x 66 = 132

Total number of rectangle = ⁹C₂ ⁹C₂

Required probability = \(\frac{132 \times 4}{9 \times 8 \times 9 \times8} = \frac{11}{108}\)