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A tea party is arranged for 16 people along the two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. In how many ways can they be seated?
- a)10C4x 8!
- b)10P4x (8!)2
- c)10C4 x (8!)2
- d)4! x 2! x (8!)2
Correct answer is option 'C'. Can you explain this answer?
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To solve this problem, we need to consider the arrangement of the four men on one side and the two men on the other side separately.
Arrangement of Four Men:
There are 8 chairs on one side of the table, and we need to arrange 4 men on these chairs. We can select 4 men out of the 10 men available in 10C4 ways. Therefore, the number of ways to arrange the four men on one side is 10C4.
Arrangement of Two Men:
Similarly, there are 8 chairs on the other side of the table, and we need to arrange 2 men on these chairs. We can select 2 men out of the remaining 6 men in 6C2 ways. Therefore, the number of ways to arrange the two men on the other side is 6C2.
Arrangement of Remaining 10 People:
After arranging the four men and two men on the two sides of the table, we are left with 10 people. These 10 people can be arranged in 8! ways since there are 8 chairs on each side.
Total Number of Ways:
To find the total number of ways to arrange the people, we need to multiply the number of ways for each step. Therefore, the total number of ways is:
10C4 * 6C2 * 8!
Simplifying the expression:
10C4 = 10! / (4! * 6!) = 10 * 9 * 8 * 7 / (4 * 3 * 2 * 1) = 210
6C2 = 6! / (2! * 4!) = 6 * 5 / (2 * 1) = 15
So, the total number of ways to arrange the people is:
210 * 15 * 8! = 10C4 * 6C2 * 8!
Therefore, the correct answer is option c) 10C4 * 6C2 * 8!
Arrangement of Four Men:
There are 8 chairs on one side of the table, and we need to arrange 4 men on these chairs. We can select 4 men out of the 10 men available in 10C4 ways. Therefore, the number of ways to arrange the four men on one side is 10C4.
Arrangement of Two Men:
Similarly, there are 8 chairs on the other side of the table, and we need to arrange 2 men on these chairs. We can select 2 men out of the remaining 6 men in 6C2 ways. Therefore, the number of ways to arrange the two men on the other side is 6C2.
Arrangement of Remaining 10 People:
After arranging the four men and two men on the two sides of the table, we are left with 10 people. These 10 people can be arranged in 8! ways since there are 8 chairs on each side.
Total Number of Ways:
To find the total number of ways to arrange the people, we need to multiply the number of ways for each step. Therefore, the total number of ways is:
10C4 * 6C2 * 8!
Simplifying the expression:
10C4 = 10! / (4! * 6!) = 10 * 9 * 8 * 7 / (4 * 3 * 2 * 1) = 210
6C2 = 6! / (2! * 4!) = 6 * 5 / (2 * 1) = 15
So, the total number of ways to arrange the people is:
210 * 15 * 8! = 10C4 * 6C2 * 8!
Therefore, the correct answer is option c) 10C4 * 6C2 * 8!
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A tea party is arranged for 16 people along the two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. In how many ways can they be seated?a)10C4x 8!b)10P4x (8!)2c)10C4 x (8!)2d)4! x 2! x (8!)2Correct answer is option 'C'. Can you explain this answer?
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A tea party is arranged for 16 people along the two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. In how many ways can they be seated?a)10C4x 8!b)10P4x (8!)2c)10C4 x (8!)2d)4! x 2! x (8!)2Correct answer is option 'C'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A tea party is arranged for 16 people along the two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. In how many ways can they be seated?a)10C4x 8!b)10P4x (8!)2c)10C4 x (8!)2d)4! x 2! x (8!)2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tea party is arranged for 16 people along the two sides of a long table with 8 chairs on each side. Four men wish to sit on one particular side and two on the other side. In how many ways can they be seated?a)10C4x 8!b)10P4x (8!)2c)10C4 x (8!)2d)4! x 2! x (8!)2Correct answer is option 'C'. Can you explain this answer?.
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