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seven people are seated in a row. probability that two particular persons A &B are seated at the end is?

(a) 1/14      (b)1/21            (c)1/81           (d)2/15

ANS:

To find the probability that two particular persons, A and B, are seated at the end of a row when seven people are seated in total, we can consider the total number of ways the seven people can be arranged and then calculate the number of favorable outcomes where A and B are seated at the end.

Total number of ways to arrange 7 people in a row = 7!

Now, when A and B are seated at the end, they can be arranged among themselves in 2! ways. Additionally, the remaining 5 people can be arranged in 5! ways.

Therefore, the number of favorable outcomes where A and B are seated at the end = 2! * 5!

The probability that A and B are seated at the end = (Number of favorable outcomes) / (Total number of outcomes) = (2! * 5!) / 7!

Calculating the values: 2! = 2 5! = 120 7! = 5040

Substitute these values into the probability formula: Probability = (2 * 120) / 5040 Probability = 240 / 5040 Probability = 1 / 21

Therefore, the probability that two particular persons A and B are seated at the end of the row is 1/21.

Comments

Abhilash Thampy said…
To find the probability that two particular persons, A and B, are seated at the end of a row when seven people are seated in total, we can consider the total number of ways the seven people can be arranged and then calculate the number of favorable outcomes where A and B are seated at the end.

Total number of ways to arrange 7 people in a row = 7!

Now, when A and B are seated at the end, they can be arranged among themselves in 2! ways. Additionally, the remaining 5 people can be arranged in 5! ways.

Therefore, the number of favorable outcomes where A and B are seated at the end = 2! * 5!

The probability that A and B are seated at the end = (Number of favorable outcomes) / (Total number of outcomes) = (2! * 5!) / 7!

Calculating the values: 2! = 2 5! = 120 7! = 5040

Substitute these values into the probability formula: Probability = (2 * 120) / 5040 Probability = 240 / 5040 Probability = 1 / 21

Therefore, the probability that two particular persons A and B are seated at the end of the row is 1/21.
April 4, 2024 at 11:23 PM
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