If a party of n persons sit at a round table, then odds against two specified individuals sitting ne

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14.Probability

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If a party of $n$ persons sit at a round table, then the odds against two specified individuals sitting next to each other are

$2\,\,:\,\,(n - 3)$

$(n - 3)\,\,:\,\,2$

$(n - 2)\,\,:\,\,2$

$2\,\,:\,\,(n - 2)$

Solution

(b) The total number of ways in which $n$ persons can sit at a round table $ = (n – 1)\,\,!.$
$\therefore $ Favourable number of cases $ = 2\,\,!\,\,(n – 2)\,\,!$
Thus the required probability $ = \frac{{2\,\,!\,\,(n – 2)\,\,!}}{{(n – 1)\,\,!}} = \frac{2}{{n – 1}}$
Hence the odds against are $(1 – p):p$ or $(n – 3):2.$

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Solution

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