A student was asked to generate a regular expression to denote the student

letter grades that recognize al the strings made up of the symbols $\{$A$,$ B$,$ C$,$ D$,$ F$\}$ with no more than two F grades. He designed the following:

$($A $+$B $+$C $+$D$)*$F$($A $+$B $+$C $+$D$)*$F

But the Professor found that ti is incorrect. i$.$ Why is it incorrect?

Debug the incorrect regular expression to accept the language.