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?
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?
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?
Show 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.
1. Positioning events with ordering constraints
2. Assigning people under availability rules.
Count possibilities in each layer consistently.
Updated On: Nov 30, 2025
- 12
- 15
- 18
- 20
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
We schedule lectures L1--L5 on Mon--Fri, and assign professors A--E (each exactly once).
Step 1: A must teach L3.
So L3 is fixed on whichever day A is assigned.
Step 2: Order restriction L2 after L5.
Valid (L5, L2) day-pairs:
(Mon,Tue), (Mon,Wed), (Mon,Thu), (Mon,Fri),
(Tue,Wed), (Tue,Thu), (Tue,Fri),
(Wed,Thu), (Wed,Fri),
(Thu,Fri).
A total of 10 possible placements.
Step 3: Professor restrictions.
C cannot teach on Wed or Fri -- C must be Mon/Tue/Thu.
B cannot teach L4 -- whichever day L4 lands on cannot get B.
D must teach before E -- day(D) < day(E).
Step 4: Combine lecture placements with professor placements.
For each of the 10 valid positions of (L5, L2), we must assign:
- L3 to A.
- Remaining lectures L1, L4, L5, L2 to professors B, C, D, E respecting rules.
In each arrangement:
• C may be assigned only if the lecture day is Mon/Tue/Thu.
• B cannot take L4.
• D and E must satisfy the day order.
Careful counting case-by-case (over each of the 10 allowed (L5, L2) placements) gives: \[ \text{Total valid schedules} = 18. \] Final Answer: 18
Step 1: A must teach L3.
So L3 is fixed on whichever day A is assigned.
Step 2: Order restriction L2 after L5.
Valid (L5, L2) day-pairs:
(Mon,Tue), (Mon,Wed), (Mon,Thu), (Mon,Fri),
(Tue,Wed), (Tue,Thu), (Tue,Fri),
(Wed,Thu), (Wed,Fri),
(Thu,Fri).
A total of 10 possible placements.
Step 3: Professor restrictions.
C cannot teach on Wed or Fri -- C must be Mon/Tue/Thu.
B cannot teach L4 -- whichever day L4 lands on cannot get B.
D must teach before E -- day(D) < day(E).
Step 4: Combine lecture placements with professor placements.
For each of the 10 valid positions of (L5, L2), we must assign:
- L3 to A.
- Remaining lectures L1, L4, L5, L2 to professors B, C, D, E respecting rules.
In each arrangement:
• C may be assigned only if the lecture day is Mon/Tue/Thu.
• B cannot take L4.
• D and E must satisfy the day order.
Careful counting case-by-case (over each of the 10 allowed (L5, L2) placements) gives: \[ \text{Total valid schedules} = 18. \] Final Answer: 18
Was this answer helpful?
0
0
Top Questions on Logical Reasoning
Disregard commonly known facts. Which conclusion would follow on the basis of given statements only?
Statement (I): Some bottles are car. Some cars are cycle.
Conclusion: \[\begin{array}{rl} \bullet & \text{[(I)] Some bottles are cycle is a possibility.} \\ \bullet & \text{[(II)] All bottles are cycle.} \\ \end{array}\]
- CUET (PG) - 2025
- General
- Logical Reasoning
- There are five men - A, B, C, D and E, six women - P, Q, R, S, T and Z, A, B, and R are advocates. S, Q, P, D and C are doctors and the rest are teachers. A team has to be selected from these eleven persons subject to the following conditions: \[\begin{array}{rl} \bullet & \text{[(I)] A, P and Z have to be together.} \\ \bullet & \text{[(II)] B cannot go with D or R.} \\ \bullet & \text{[(III)] E and Q have to be together.} \\ \bullet & \text{[(IV)] C and T have to be together.} \\ \bullet & \text{[(V)] D and P cannot go together.} \\ \bullet & \text{[(VI)] C cannot go with Q.} \\ \end{array}\] If the team formed consists of two male advocates, two lady doctors and one teacher, the members of the team can be:
- CUET (PG) - 2025
- General
- Logical Reasoning
- P, Q, R, S, T, A and B are consecutive integers (not necessarily in that order), such that the smallest of these is greater than 60 and the greatest is less than 70. It is known that:
(I) A and B both are prime numbers.
(II) T is a multiple of 9.
(III) Both the digits of P are same.
(IV) The average of R and S is 63 and the difference between R and S is 2.
What is the sum of A and Q if A is smaller than B?- CUET (PG) - 2025
- General Management
- Logical Reasoning
- P, Q, R, S, T are five consecutive integers (not necessarily in that order), such that the smallest of these is greater than 60 and the greatest is less than 70. It is known that: (i) A and B both are prime numbers. (ii) T is a multiple of 9. (iii) Both the digits of P are same. (iv) The average of R and S is 63 and the difference between R and S is 2. What is the sum of the digits of the number Q?
- CUET (PG) - 2025
- General Management
- Logical Reasoning
- Eight boxes - A, B, C, D, P, Q, R and S are stacked vertically but not necessarily in the same order. Which among them is kept immediately above R?
Statement (I): Only three boxes are kept above D and only one box is kept between D and Q. Q is kept lower than D and is immediately below P.
Statement (II): Only one box is kept between A and C. C is kept three boxes above Q. As many boxes are kept above B as are kept below R.- CUET (PG) - 2025
- General Management
- Logical Reasoning
View More Questions
Questions Asked in CAT exam
- The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
- Para Summary
- The number of distinct integers $n$ for which $\log_{\left(\frac14\right)}(n^2 - 7n + 11)>0$ is:
- CAT - 2025
- Linear Inequalities
- In the set of consecutive odd numbers $\{1, 3, 5, \ldots, 57\}$, there is a number $k$ such that the sum of all the elements less than $k$ is equal to the sum of all the elements greater than $k$. Then, $k$ equals?
- CAT - 2025
- Number Systems
- The number of distinct pairs of integers $(x, y)$ satisfying the inequalities $x>y \ge 3$ and $x + y<14$ is:
- CAT - 2025
- Number Systems
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is:
- CAT - 2025
- Linear Inequalities
View More Questions