If $5$ squares are chosen at random from a chess board, what is the probability that they lie on a diagonal line?
Probability – Probability that 5 Squares Lie Along a Diagonal Line
probability
probability
If $5$ squares are chosen at random from a chess board, what is the probability that they lie on a diagonal line?
Best Answer
HINT:
There are $64$ squares altogether; how many ways are there to choose $5$ of them?
There are $15$ diagonals in each direction, but only $7$ of them are long enough to contain $5$ squares. Specifically, in each direction there are two diagonals of length $5$, two of length $6$, two of length $7$, and one of length $8$. How many $5$-element subsets are there of each of these diagonals?
The total in (2) is the number of sets of $5$ squares that lie on a diagonal. The total in (1) is the total number of sets of $5$ squares. Combine these two numbers to get the desired probability.