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Q.
A telegraph has $5$ arms and each arm is capable of $4$ distinct positions, including the position of rest. The total number of signals that can be made is
Permutations and Combinations
Solution:
Each arm can be set in $4$ ways.
$\therefore $ Five arms can be set in $4 \times 4 \times 4 \times 4 \times 4$ ways.
But this includes the way when all the arms are in the position of rest, when no signal is sent.
Hence, required number of signals
$=4^{5}-1=1024-1=1023$