Q.32. Probability

AQuestion 32.
From a chess board three blocks are chosen at random. What is the probability that the three blocks are from the same diagonal?

 Answer 32.
Total no. of ways of choosing three blocks out of 64 blocks,
n = 64C3 = 41664.
Three blocks can be chosen from diagonals from left to right in
2 (3C3 + 4C3 + 5C3 + 6C3 + 7C3) + 8C3 ways = 196.
Three blocks can be chosen from diagonals from right to left in 196 ways.
Total number of ways of choosing three blocks such that they are from the same diagonal,
r = 196 + 196 = 392.
By classical definition of probability,
required probability
= r / n
= 392 / 41664
= 7 / 744.

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