Suppose n ge 3 persons are sitting in a row. | vedclass

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Question

(a) Let there be $n$ persons and $(n - 2)$ persons not selected are arranged in places stated above by stars and the selected $2$ persons can be arran

Vedclass · Accepted Answer

$1 - \frac{2}{n}$

Vedclass · Answer

(a) Let there be $n$ persons and $(n - 2)$ persons not selected are arranged in places stated above by stars and the selected $2$ persons can be arranged at places stated by dots (dots are $n - 1$ in number)

So the favourable ways are $^{n - 1}{C_2}$ and the total ways are $^n{C_2}$, so

$ 	imes \bullet 	imes \bullet 	imes \bullet 	imes \bullet 	imes \bullet 	imes $

$P = \frac{{^{n - 1}{C_2}}}{{^n{C_2}}} $

$= \frac{{(n - 1)\,!\,2\,!\,(n - 2)\,!}}{{(n - 3)\,!\,2\,!\,n\,!}} = \frac{{n - 2}}{n} = 1 - \frac{2}{n}$.

Suppose $n \ge 3$ persons are sitting in a row. Two of them are selected at random. The probability that they are not together is

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