Question

$5$ telegrams are to be distributed at random over $10$ communication channels. The probability that not more than one telegram will be sent over each channel is :

• A. $\frac{{}^{10}{C}_5}{{10}^5}$
• B. $\frac{5!}{{10}^5}$
• C. $\frac{{}^{10}{P}_5}{{10}^5}$
• D. $\frac{5^{10}}{{10}^5}$

Answer 1

The correct option is C $\frac{{}^{10}{P}_5}{{10}^5}$

Total ways in which one telegram can be sent $=10$
Total ways in which $5$ telegrams can be sent $=10\ast 10\ast 10\ast 10\ast 10$
$={10}^5$
We will select $5$ channels from $10$ channels and assign each telegram each channel to keep them isolated
No. of ways in which no two telegrams get the same channel $=10C_5\ast 5!$
$=10P_5$
$\Rightarrow P=10P_5/{10}^5$