Three squares are chosen at random from the 3 × 3 grid below, and a cross is placed in each chosen square - HSC - SSCE Mathematics Extension 1 - Question 10 - 2017 - Paper 1

Next, we find the number of favorable outcomes where all three crosses are in the same row, column, or diagonal.

1. Rows: There are 3 rows, and in each row, we can choose all 3 squares in exactly one way. Therefore:

   • Favourable outcomes for rows = 3.

2. Columns: Similar to rows, there are also 3 columns:

   • Favourable outcomes for columns = 3.

3. Diagonals: There are 2 diagonals:

   • Favourable outcomes for diagonals = 2.

Adding these gives us:

$3 + 3 + 2 = 8$

We can now calculate the probability of the three crosses being in the same row, column or diagonal:

$P = \frac{\text{Number of favorable outcomes}}{\text{Total possible selections}} = \frac{8}{84} = \frac{2}{21}$

Thus, the final answer is B. 2/21.