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

We first use the time-slot constraints.
Q must be in T1 or T4. R must be interviewed before S.
C4 can interview only in T2 or T3, so candidates in T1 and T4 cannot be assigned to C4.
Last-year restrictions forbid: C1--P, C2--Q, C3--R, C4--S.
P also cannot be interviewed by C1 or C3, so P must be assigned to C2 or C4, with C4 allowed only in T2 or T3.
Case 1: Q in T1.
Q cannot be interviewed by C2 (last year) or C4 (C4 only works in T2/T3), so Q is assigned to C1 or C3.
Enumerating all valid placements for R before S and assigning P under company restrictions gives 4 valid schedules.
Case 2: Q in T4.
A similar analysis applies. Q cannot be assigned to C2 or C4, and R--S ordering must be respected.
Again, 4 valid schedules satisfy all constraints.
Total valid schedules: $4 + 4 = 8$.
Final Answer: 8