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Bunuel
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Eighteen guests have to be seated half on each side of a long table. 23 Feb 2021, 06:30
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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70% (01:51) correct 30% (02:14) wrong based on 180 sessions

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Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit one particular side and three other on the other side. Determine the number of ways in which the sitting arrangements can be made.

A. 9P4 × 9P3 × (9)!
B. 9P4 × 9P3 × (10)!
C. 9P4 × 9P3 × (11)!
D. 9P4 × 9P3 × (12)!
E. 9P4 × 9P3 × (13)!

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C
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Eighteen guests have to be seated half on each side of a long table. 23 Feb 2021, 10:07
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Number of ways to choose 5 people out of 11 = 11C5
Number of arrangements on each side of the table = 9!

Total possible arrangements = 11C5 * 9! * 9! = (11!/5!*6!)*9!*9! = 11! * (9!/5!) * (9!/6!) = 11! * 9P4 * 9P3
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Eighteen guests have to be seated half on each side of a long table. 02 Mar 2021, 10:50
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Bunuel , chetan2u
Could you please help me with this question.
How it is 12! , I am not able to get it.

Thanks in advance for your help.

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Eighteen guests have to be seated half on each side of a long table. 02 Mar 2021, 13:37
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Mona2019 it looks like the answer choices have a typo, it should be 11! for C and 12! for D etc.

My solution:

Slot in the four guests first, they have 9 seats to choose from so that is 9P4 options (9*8*7*6).
The next three guests on the other side of the table have 9 seats to choose from as well, that is 9P3 options for them.

Finally there are 11 seats to fill in with 11 guests, so 11P11 or 11! for those 11 people.

Since these three groups of guests are independent, we multiply all of the above to get 9P4 * 9P3 * 11!.

Ans: C
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Eighteen guests have to be seated half on each side of a long table. 02 Mar 2021, 22:17
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I thought I must be missing something .

Thank you for replying and clearing my doubt . TestPrepUnlimited

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Eighteen guests have to be seated half on each side of a long table. 13 Mar 2021, 15:57
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Bunuel
Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit one particular side and three other on the other side. Determine the number of ways in which the sitting arrangements can be made.

A. 9P4 × 9P3 × (9)!
B. 9P4 × 9P3 × (10)!
C. 9P4 × 9P3 × (11)!
D. 9P4 × 9P3 × (12)!
E. 9P4 × 9P3 × (13)!

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Solution:

There are 9P4 ways for the 4 guests who want to sit on one side of the table and 9P3 ways for the 3 other guests who want to sit on the other side of the table. Since there are no restrictions for the remaining 11 guests, there are 11P11 = 11! ways for them to sit at the remaining seats. Therefore, the total number of seating arrangements is 9P4 x 9P3 x 11!.

Answer: C
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Eighteen guests have to be seated half on each side of a long table. 11 Aug 2025, 00:14
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Bunuel
Eighteen guests have to be seated half on each side of a long table. Four particular guests desire to sit one particular side and three other on the other side. Determine the number of ways in which the sitting arrangements can be made.

A. 9P4 × 9P3 × (9)!
B. 9P4 × 9P3 × (10)!
C. 9P4 × 9P3 × (11)!
D. 9P4 × 9P3 × (12)!
E. 9P4 × 9P3 × (13)!

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Number of ways of choosing and seating 4 guests out of half of 18 i.e 9 = P(9,4)
Number of ways of choosing and seating 3 guests out of half of 18 i.e 9 = P(9,3)

Remaining guests = (18-7) = 11
These can be arranged in 11! ways

Hence, C
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