Quote:

$\displaystyle \text{2. Thirty numbers are arranged in a }6 \times 5\text{ array as shown.}$

. . $\displaystyle \begin{array}{|c|c|c|c|c|} \hline 1 & 2 & 3 & 4 & 5 \\ \hline 6 & 7 & 8 & 9 & 10 \\ \hline 11 & 12 & 13 & 14 & 15 \\ \hline 16 & 17 & 18 & 19 & 20 \\ \hline 21 & 22 & 23 & 24 & 25 \\ \hline 26 & 27 & 28 & 29 & 30 \\ \hline \end{array}$

$\displaystyle \text{Calculate the number of ways to form a set of three distinct numbers so that}$

$\displaystyle \text{no two of the selected numbers are in the same row or same column.}$