nav · 2026-06-19 · 2 helpful
The total number of possible ways in which the officer could have summoned the seven persons is 4.
By analyzing the restrictions given for each individual, we can narrow down their possible days:
1. Vikas: Cannot be on Mon, Fri, Sat, Sun.
* Restrained to Tuesday, Wednesday, or Thursday.
2. Yash: Cannot be on Mon, Tue, Wed, Fri, Sun.
* Restrained to Thursday or Saturday.
3. Ritesh: Cannot be on Mon, Tue, Wed, Sun.
* Restrained to Thursday, Friday, or Saturday.
4. Kanchan: Cannot be on Mon, Tue, Thu.
5. Sanjay: Must be after Wednesday (Thu, Fri, Sat, Sun) and before Mahesh.
Initial Positions:
* Tuesday belongs to Vikas: Since Yash and Ritesh cannot be on Tuesday or Wednesday, and Kanchan cannot be on Tuesday, Vikas is the only one among them who can take Tuesday. (If Vikas took Wednesday or Thursday, Tuesday would be left without anyone fitting the constraints).
* Wednesday belongs to Kanchan: With Vikas on Tuesday, Kanchan's remaining available days from the front of the week shift. Since she cannot be on Mon, Tue, or Thu, and the weekend is needed for Sanjay/Mahesh order, she fits perfectly on Wednesday.
* Monday belongs to Richa: Mon and Sun cannot be occupied by Vikas, Yash, or Ritesh. Kanchan cannot be on Mon. Sanjay cannot be on Mon. Since Richa must be before Mahesh, Richa must take Monday, leaving Sunday for Mahesh.
This gives us a fixed baseline for 4 out of 7 days:
* Monday: Richa
* Tuesday: Vikas
* Wednesday: Kanchan
* Sunday: Mahesh
Arranging Thursday, Friday, and Saturday:
The remaining three people to place on Thursday, Friday, and Saturday are Sanjay, Yash, and Ritesh. Since Mahesh is on Sunday, Sanjay's constraint to be before Mahesh is automatically satisfied no matter which of these three days he takes.
We can arrange them in exactly 4 valid combinations:
| Mon | Tue | Wed | Thur | Fri | Sat | Sun |
| Richa | Vikas | Kanchan | Sanjay | Ritesh | Yash | Mahesh |
| Richa | Vikas | Kanchan | Ritesh | Sanjay | Yash | Mahesh |
| Richa | Vikas | Kanchan | Yash | Sanjay | Ritesh | Mahesh |
| Richa | Vikas | Kanchan | Yash | Ritesh | Sanjay| Mahesh |
Hence total number of possible ways is 4.
By analyzing the restrictions given for each individual, we can narrow down their possible days:
1. Vikas: Cannot be on Mon, Fri, Sat, Sun.
* Restrained to Tuesday, Wednesday, or Thursday.
2. Yash: Cannot be on Mon, Tue, Wed, Fri, Sun.
* Restrained to Thursday or Saturday.
3. Ritesh: Cannot be on Mon, Tue, Wed, Sun.
* Restrained to Thursday, Friday, or Saturday.
4. Kanchan: Cannot be on Mon, Tue, Thu.
5. Sanjay: Must be after Wednesday (Thu, Fri, Sat, Sun) and before Mahesh.
Initial Positions:
* Tuesday belongs to Vikas: Since Yash and Ritesh cannot be on Tuesday or Wednesday, and Kanchan cannot be on Tuesday, Vikas is the only one among them who can take Tuesday. (If Vikas took Wednesday or Thursday, Tuesday would be left without anyone fitting the constraints).
* Wednesday belongs to Kanchan: With Vikas on Tuesday, Kanchan's remaining available days from the front of the week shift. Since she cannot be on Mon, Tue, or Thu, and the weekend is needed for Sanjay/Mahesh order, she fits perfectly on Wednesday.
* Monday belongs to Richa: Mon and Sun cannot be occupied by Vikas, Yash, or Ritesh. Kanchan cannot be on Mon. Sanjay cannot be on Mon. Since Richa must be before Mahesh, Richa must take Monday, leaving Sunday for Mahesh.
This gives us a fixed baseline for 4 out of 7 days:
* Monday: Richa
* Tuesday: Vikas
* Wednesday: Kanchan
* Sunday: Mahesh
Arranging Thursday, Friday, and Saturday:
The remaining three people to place on Thursday, Friday, and Saturday are Sanjay, Yash, and Ritesh. Since Mahesh is on Sunday, Sanjay's constraint to be before Mahesh is automatically satisfied no matter which of these three days he takes.
We can arrange them in exactly 4 valid combinations:
| Mon | Tue | Wed | Thur | Fri | Sat | Sun |
| Richa | Vikas | Kanchan | Sanjay | Ritesh | Yash | Mahesh |
| Richa | Vikas | Kanchan | Ritesh | Sanjay | Yash | Mahesh |
| Richa | Vikas | Kanchan | Yash | Sanjay | Ritesh | Mahesh |
| Richa | Vikas | Kanchan | Yash | Ritesh | Sanjay| Mahesh |
Hence total number of possible ways is 4.