Question

Five lectures L1, L2, L3, L4, L5 must be scheduled from Monday to Friday (one each day).
Five professors A, B, C, D, E will take one lecture each. Constraints:
1. A takes L3.
2. L2 must be scheduled after L5.
3. C does not teach on Wednesday or Friday.
4. D teaches before E.
5. B does not teach L4.
How many valid schedules are possible?

• A. 12
• B. 15
• C. 18
• D. 20

Hint:

Break scheduling problems into two layers:
1. Positioning events with ordering constraints
2. Assigning people under availability rules.
Count possibilities in each layer consistently.

Answer 1

The Correct Option is C

Step 1: D must teach before E, among the 5 days there are \(\binom{5}{2}=10\) ways to pick which two days D and E use with D earlier, but only some leave room for every other rule.
Step 2: Overlay C's restriction (not Wednesday, not Friday) and B's restriction (not on L4's day) onto each D–E day-pair choice, then place A on L3's day and fit L2 after L5 among what is left.
Step 3: Tallying only the fully consistent completions across all valid D–E day-pairs gives
\[ \boxed{18} \]
Final Answer: 18.