Probability
Probability
star_batch_jee_advanced_2025
Grade None
Question:
Three smallest squares are chosen randomly on a chess board are the probability that these squares have exactly two corners, but no side common is:
$\frac{80}{^{64}C_3}$
$\frac{72}{^{64}C_3}$
$\frac{6^3}{^{64}C_3}$
None of these
Step-by-Step Solution
Key Concept: Fix the shaded corner square, then count ways to choose 2 more corners from remaining 4.
If a shaded square is chosen, 2 additional corner squares must be selected from 4 remaining corner squares, which can be done in $^4C_2 = 6$ ways. The probability is $ rac{^4C_1 \cdot 6^2}{^{64}C_3}$.
Correct Answer: 3