Unit $5$ Section: Permutations and Combinations

$4.$ First$-$year university students in the science faculty must take an English course, $3$ other courses from column $A,$ and $2$ courses from column B as shown in the chart.

$\backslash$table$[[$Column A$,$Column B$],[$Biology$,$Accounting$],[$Calculus$,$Commercial Law$],[$Chemistry$,$Computer Programming$],[$Physics$,$Public Speaking$],[,$Psychology$],[,$Sociology$]]$

Determine the number of different program choices available to these students.