Question

M telegrams are to be distributed at random over N communication channels $(N>M)$ . The probability that not more than one telegram will be sent over each channel

• A. $\frac{{}^N{C}_M}{N^M}$
• B. $\frac{{}^M{C}_N}{N^N}$
• C. $\frac{{}^N{P}_M}{N^M}$
• D. $\frac{{}^M{P}_N}{N^H}$

Answer 1

The correct option is C $\frac{{}^N{P}_M}{N^M}$

We will select M places out of N channels and permute all M telegrams in these places
Hence total number of ways =$\left(\begin{array}{c}N\\ M\end{array}\right)\times M!$
And total number of ways of distribution =Each telegram having N options =$N^M$
Hence probability $P=\frac{\left(\begin{array}{c}N\\ M\end{array}\right)\times M!}{N^M}$