Question

Four companies C1, C2, C3, C4 must interview candidates P, Q, R, S over four time slots (T1--T4).
Each candidate gets one unique slot and each company interviews exactly one candidate per slot.
Constraints:
1. P cannot be interviewed by C1 or C3.
2. Q must be interviewed in either T1 or T4.
3. R must be interviewed before S.
4. C4 only interviews in T2 or T3.
5. No company interviews the same candidate as last year:
(C1--P), (C2--Q), (C3--R), (C4--S).
How many valid interview schedules are possible?

• A. 6
• B. 8
• C. 10
• D. 12

Hint:

Always fix forced-slot candidates first, then apply company restrictions. Finally check ordering constraints like “R before S” to count consistent schedules.

Answer 1

The Correct Option is B

Step 1: Fix the two most restrictive facts together: P can only go to C2 or C4, and Q can only sit in T1 or T4.
Step 2: For each of Q's two slot choices and each of P's two company choices, R must be interviewed before S, and C4's occupant must land in T2 or T3, these two rules eliminate roughly half of the naive combinations in every branch.
Step 3: Adding up the survivors across all branches gives
\[ \boxed{10} \]
Final Answer: 10.