n (> 3) persons are sitting in a row. Two of them are selected. Write

1.	n (> 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.
Answer» Let E denote the event that the selected persons are sitting together. As 2 persons can be selected out of n in ⁿC₂ ways Out of n persons we can select two persons sitting together in (n-1) ways. Because we have to select only one person next person is going to be automatically selected. We can’t select last person because no one is sitting next to him. ∴ 1 person out of n-1 persons can be selected in (n-1) ways. ∴ P(E) = \(\frac{n-1}{^nC_2}\) = \(\frac{2(n-1)}{n(n-1)}\) = \(\frac{2}{n}\) Thus, P(E) = \(\frac{2}{n}\)

n (> 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

Answer»

Let E denote the event that the selected persons are sitting together.

As 2 persons can be selected out of n in ⁿC₂ ways

Out of n persons we can select two persons sitting together in (n-1) ways.

Because we have to select only one person next person is going to be automatically selected.

We can’t select last person because no one is sitting next to him.

∴ 1 person out of n-1 persons can be selected in (n-1) ways.

∴ P(E) = \(\frac{n-1}{^nC_2}\) = \(\frac{2(n-1)}{n(n-1)}\) = \(\frac{2}{n}\)

Thus, P(E) = \(\frac{2}{n}\)

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n (&gt; 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

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n (> 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.