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A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?
- a)21C6 * 120 * 14!
- b)21C15 * 14!
- c)21C6 *15! * 6!
- d)none
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A businessman hosts a dinner to 21 guests. He is having 2 round tables...
Total guest = 21, guests are
seated in round table respectively are 15 and 6
Total ways = 21C15 x 14!5!
seated in round table respectively are 15 and 6
Total ways = 21C15 x 14!5!
Most Upvoted Answer
A businessman hosts a dinner to 21 guests. He is having 2 round tables...
Total guest = 21, guests are
seated in round table respectively are 15 and 6
Total ways = 21C15 x 14!5!
seated in round table respectively are 15 and 6
Total ways = 21C15 x 14!5!
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A businessman hosts a dinner to 21 guests. He is having 2 round tables...
The Problem:
A businessman is hosting a dinner for 21 guests. He has two round tables available, one that can accommodate 15 persons and another that can accommodate 6 persons. The question asks for the number of ways the dinner can be hosted.
Solution:
To find the number of ways to host the dinner, we need to consider the number of ways to seat the guests at each table.
Table 1:
The first table can accommodate 15 persons. To find the number of ways to seat 15 guests at this table, we can use the concept of combinations. The number of ways to choose 15 guests from a group of 21 is given by the combination formula "21C15". Therefore, the number of ways to seat the guests at table 1 is "21C15".
Table 2:
The second table can accommodate 6 persons. Similarly, the number of ways to seat 6 guests at this table is given by the combination formula "21C6".
Arrangement of Guests:
Once the guests are seated at each table, we need to consider the arrangement of the guests within each table. For table 1, there are 15 seats, so the number of ways to arrange the guests is 15!. Similarly, for table 2, there are 6 seats, so the number of ways to arrange the guests is 6!.
Total Number of Ways:
To find the total number of ways to host the dinner, we need to multiply the number of ways for each table and the arrangement of guests within each table. Therefore, the total number of ways is given by:
"21C15 * 15! * 21C6 * 6!"
Simplification:
Let's simplify the expression to see if it matches any of the given options:
- "21C15 * 15! * 21C6 * 6!" can be rewritten as "21! / (15! * 6!) * 15! * 21! / (6! * 15!)".
- The 15! terms in the numerator and denominator cancel out, as well as the 6! terms.
- This leaves us with "21! * 21! / (15! * 15! * 6!)".
Comparing this with the given options:
a) 21C6 * 120 * 14!: This option does not match the simplified expression.
b) 21C15 * 14!: This option does not match the simplified expression.
c) 21C6 * 15! * 6!: This option matches the simplified expression.
d) None: This option does not match the simplified expression.
Therefore, the correct answer is option 'C': 21C6 * 15! * 6!.
A businessman is hosting a dinner for 21 guests. He has two round tables available, one that can accommodate 15 persons and another that can accommodate 6 persons. The question asks for the number of ways the dinner can be hosted.
Solution:
To find the number of ways to host the dinner, we need to consider the number of ways to seat the guests at each table.
Table 1:
The first table can accommodate 15 persons. To find the number of ways to seat 15 guests at this table, we can use the concept of combinations. The number of ways to choose 15 guests from a group of 21 is given by the combination formula "21C15". Therefore, the number of ways to seat the guests at table 1 is "21C15".
Table 2:
The second table can accommodate 6 persons. Similarly, the number of ways to seat 6 guests at this table is given by the combination formula "21C6".
Arrangement of Guests:
Once the guests are seated at each table, we need to consider the arrangement of the guests within each table. For table 1, there are 15 seats, so the number of ways to arrange the guests is 15!. Similarly, for table 2, there are 6 seats, so the number of ways to arrange the guests is 6!.
Total Number of Ways:
To find the total number of ways to host the dinner, we need to multiply the number of ways for each table and the arrangement of guests within each table. Therefore, the total number of ways is given by:
"21C15 * 15! * 21C6 * 6!"
Simplification:
Let's simplify the expression to see if it matches any of the given options:
- "21C15 * 15! * 21C6 * 6!" can be rewritten as "21! / (15! * 6!) * 15! * 21! / (6! * 15!)".
- The 15! terms in the numerator and denominator cancel out, as well as the 6! terms.
- This leaves us with "21! * 21! / (15! * 15! * 6!)".
Comparing this with the given options:
a) 21C6 * 120 * 14!: This option does not match the simplified expression.
b) 21C15 * 14!: This option does not match the simplified expression.
c) 21C6 * 15! * 6!: This option matches the simplified expression.
d) None: This option does not match the simplified expression.
Therefore, the correct answer is option 'C': 21C6 * 15! * 6!.
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A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer?.
A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer? for Mathematics 2025 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Mathematics 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer?.
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A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer?, a detailed solution for A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer? has been provided alongside types of A businessman hosts a dinner to 21 guests. He is having 2 round tables which can accommondate 15 and 6 persons. How many ways are there to host dinner?a)21C6 * 120 * 14!b)21C15 * 14!c)21C6 *15! * 6!d)noneCorrect answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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