There are m persons sitting in a row. Two of them are selected at random. The probability that the two selected persons are not together

1 - \frac{^{m - 1} c_{2}}{m_{C_{2}}}

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1 - \frac{m - 1}{m_{C_{2}}}

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1 - \frac{m - 3}{m_{C_{2}}}

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\frac{m - 3}{m_{C_{2}}}

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Solution

The correct option is B $1 - \frac{m - 1}{m_{C_{2}}}$
$P (n o t t o g e t h e r) = 1 - P (t o g e t h e r)$
$(m - 1)$ pairs of people sitting adjacent can be formed
P(two people are seated together) $= (m - 1) /^{m} C_{2}$
So,
P(not together) $= 1 - \frac{m - 1}{^{m} C_{2}}$

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