A local post office is to send M telegrams which are distributed at random over N communication channels, (N > M). Each telegram is sent over any channel with equal probability. Chance that not more than one telegram will be sent over each channel is

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$\frac{^{N} C_{M} \times N!}{M^{N}}$

$\frac{^{N} C_{M} \times M!}{N^{M}}$

$1 - \frac{^{N} C_{M} \times M!}{M^{N}}$

$1 - \frac{^{N} C_{M} \times N!}{N^{M}}$

answer is B.

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Detailed Solution

Since lines are more than telegrams, $^{N} C_{M}$ are those lines where telegrams will be sent.

So, number of favourable cases $=^{N} C_{M} \times M!$

Total number of cases = N^M [As first telegram can go in any one of n lines]

So, required probability $= \frac{^{N} C_{M} \times M!}{N^{M}}$

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