Answer
Now starting from the 1st lecture we go on picking lectures in such a way that the lectures that are being picked have starting time later than the finishing time of the chosen lecture
this gives us the sequence
$(1) -(3) -(6) -(9) $
in this way, we can pick the lectures.
Work Step by Step
Let's first arrange the lectures in the order of their finishing time
$1) 9 : 00 - 9:45$
$2) 9 : 30 - 10:00$
$3) 9 : 50 - 10:15$
$4) 10 : 10 - 10:25$
$5) 10 : 00 - 10:30$
$6) 10 : 15 - 10:45$
$7) 10 : 30 - 10:55$
$8) 10 : 30 - 11:00$
$9)11 : 00 - 11:15$
$10) 10 : 55 -11:25$
$11) 10 : 45 -11:30$
Now starting from the 1st lecture we go on picking lectures in such a way that the lectures that are being picked have starting time later than the finishing time of the chosen lecture
this gives us the sequence
$(1) -(3) -(6) -(9) $
in this way, we can pick the lectures.