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There are 20 people sitting around a rectangular dining table, 10 on one side facing the other 10 on the opposite side, in such a way that each person knows the person sitting exactly opposite to him and the two persons sitting beside him. Four persons are chosen at a ran dom such that there are at least 3 pairs of people knowing each other. Find the probability that there are four pairs of people knowing each other.?
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There are 20 people sitting around a rectangular dining table, 10 on o...
Solution:

Given:

- 20 people sitting around a rectangular dining table, 10 on one side facing the other 10 on the opposite side, in such a way that each person knows the person sitting exactly opposite to him and the two persons sitting beside him.
- We need to find the probability that there are four pairs of people knowing each other when four persons are chosen at random such that there are at least 3 pairs of people knowing each other.

To find the probability, we need to calculate the total number of ways of choosing 4 persons out of 20 and the number of ways in which at least 3 pairs of people know each other, and 4 pairs of people know each other.

Total number of ways of choosing 4 persons out of 20:

- The total number of ways of choosing 4 persons out of 20 is given by 20C4 = (20*19*18*17)/(4*3*2*1) = 4845.

Number of ways in which at least 3 pairs of people know each other:

- When 4 persons are chosen at random, there are two possibilities: either there are 3 pairs of people who know each other, or there are 4 pairs of people who know each other.
- Let's first consider the case where there are 3 pairs of people who know each other.
- If there are 3 pairs of people who know each other, then the fourth person can be chosen in 16 ways, as he/she cannot be one of the persons who know each other.
- Therefore, the number of ways in which there are 3 pairs of people who know each other is 20*1*1*16 = 320.
- Now, let's consider the case where there are 4 pairs of people who know each other.
- If there are 4 pairs of people who know each other, then the four persons can be chosen in 10 ways, as there are 10 pairs of people who know each other.
- Therefore, the number of ways in which there are 4 pairs of people who know each other is 10.
- Therefore, the total number of ways in which at least 3 pairs of people know each other is 320 + 10 = 330.

Probability of getting 4 pairs of people knowing each other:

- The probability of getting 4 pairs of people knowing each other is given by the number of ways in which there are 4 pairs of people who know each other divided by the total number of ways of choosing 4 persons out of 20.
- Therefore, the probability of getting 4 pairs of people knowing each other is 10/4845 = 2/969.

Therefore, the probability of getting 4 pairs of people knowing each other when four persons are chosen at random such that there are at least 3 pairs of people knowing each other is 2/969.
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Directions for Questions: Answer the questions on the basis of the information given below.Eight persons are sitting at a rectangular table such that four persons are sitting along each of the longer sides of the table. Each person works in a different bank among PNB, SBI, HDFC, ICICI, CBI, BOB, BOI and Citi, and holds a different designation among IT Officer, Marketing Officer, Law Officer, Agricultural Officer, Rajbhasha Adhikari, Technical Officer, Finance Officer and HR Manager, not necessarily in the same order. It is also known that:I. The Finance Officer, who works in BOI, is sitting to the immediate left of the HR Manager.II. The Marketing Officer, who works in SBI, is sitting opposite the Technical Officer.III. The Agricultural Officer, who works in ICICI, is sitting diagonally opposite the Rajbhasha Adhikari, who is sitting to the immediate left of the Technical Officer.IV. The Law Officer, who works in HDFC, is sitting to the immediate left of the Marketing officer.V. The persons who work in PNB and HDFC are sitting along the same side of the table.VI. The Rajbhasha Adhikari, who works in CBI, is sitting at one of the extreme ends in his row.(2013)Q.The person who is sitting opposite the Law Officer works in

Directions for Questions: Answer the questions on the basis of the information given below.Eight persons are sitting at a rectangular table such that four persons are sitting along each of the longer sides of the table. Each person works in a different bank among PNB, SBI, HDFC, ICICI, CBI, BOB, BOI and Citi, and holds a different designation among IT Officer, Marketing Officer, Law Officer, Agricultural Officer, Rajbhasha Adhikari, Technical Officer, Finance Officer and HR Manager, not necessarily in the same order. It is also known that:I. The Finance Officer, who works in BOI, is sitting to the immediate left of the HR Manager.II. The Marketing Officer, who works in SBI, is sitting opposite the Technical Officer.III. The Agricultural Officer, who works in ICICI, is sitting diagonally opposite the Rajbhasha Adhikari, who is sitting to the immediate left of the Technical Officer.IV. The Law Officer, who works in HDFC, is sitting to the immediate left of the Marketing officer.V. The persons who work in PNB and HDFC are sitting along the same side of the table.VI. The Rajbhasha Adhikari, who works in CBI, is sitting at one of the extreme ends in his row.(2013)Q.Who is sitting to the immediate right of the Finance Officer?

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There are 20 people sitting around a rectangular dining table, 10 on one side facing the other 10 on the opposite side, in such a way that each person knows the person sitting exactly opposite to him and the two persons sitting beside him. Four persons are chosen at a ran dom such that there are at least 3 pairs of people knowing each other. Find the probability that there are four pairs of people knowing each other.?
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