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

Question

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 (A) 473 (B) 1023 (C) 1173 (D) None of these

Tardigrade Admin · Accepted Answer

Each arm can be set in 4 ways. ∴ Five arms can be set in 4 × 4 × 4 × 4 × 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 =45-1=1024-1=1023

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

473

1023

1173

None of these

Each arm can be set in $4$ ways.
$∴$ 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
$= 4^{5} - 1 = 1024 - 1 = 1023$

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

473

1023

1173

None of these

Each arm can be set in 4 ways. ∴ Five arms can be set in 4×4×4×4×4 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 =45−1=1024−1=1023

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

Each arm can be set in $4$ ways.
$∴$ 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
$= 4^{5} - 1 = 1024 - 1 = 1023$