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:

Options

A. `(.^(N)C_(M)xxN!)/(M^(N))`
B. `(.^(N)C_(M)xxM!)/(N^(M))`
C. `1-(.^(N)C_(M)xxM!)/(M^(N))`
D. `1-(.^(N)C_(M)xxN!)/(N^(M))`

Answer

B

Explanation

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) xx M!`
Total number of cases = `N^(M)`
[As first telegram can go in any one of n lines]
So, required probability = `(.^(N)C_(M)xxM!)/(N^(M))`