Question

This problem is a base conversion problem masquerading as a "word problem". You are responsible for controlling the stage lights at a small theater. The control box has control switches for 10 separate lights, and each switch can make its corresponding light off, red, green, yellow, or blue. How many different patterns of lighting can you set up?

Answer 1

Answer:

The number of different patterns of lighting that can be set up is 9,765,625.

Step-by-step explanation:

The options of each light switch are:

S = {Switch OFF, Red, Green, Yellow and Blue}

There are 5 ways a single light switch can be controlled.

There are 10 separate lights.

Each light has 5 options to operate.

And each light switch is independent of the others,i.e. if one light is red the other can be any of the 5 options.

Then the 10 lights has:

$5\times 5\times 5\times 5\times 5\times 5\times 5\times 5\times 5\times 5=5^{10}=9765625$

Thus, the number of different patterns of lighting that can be set up is 9,765,625.