First slide

Introduction to probability

Question

If three squares are selected at random from chessboard, then the probability that they form the letter "L" is

Moderate

A

$\frac{196}{^{64} C_{3}}$
B

$\frac{49}{^{64} C_{3}}$
C

$\frac{36}{^{64} C_{3}}$
D

$\frac{98}{^{64} C_{3}}$

Solution

We have,
$n (S) =^{64} C_{3}$
Let 'E' be the event of selecting 3 squares which form the letter 'L' .
The number of ways of selecting squares consisting of 4 unit squares is 7 x 7 = 49.
Each square with 4 unit squares form 4 L-shapes consisting of 3 unit squares. Therefore,
$n (E) = 7 \times 7 \times 4 = 196$
$∴ P (E) = \frac{196}{^{64} C_{3}}$

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