Question

A panel of four lights switches can be set in 2^4 ways. A panel of five light switches can be set in twice this many ways. In how many ways can five light switches be set? Please Help

Answer 1

$2\cdot2^4=2^5=32$

Answer 2

To solve such problems we need to know about Expressions.

Expression

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations that are formed according to rules which are dependent on the context.

The number of ways five switches can be set is 32.

Given to us

• A panel of four lights switches can be set in 2^4 ways.
• A panel of five light switches can be set in twice this many ways.

Solution

Statement 1

A panel of four lights switches can be set in 2^4 ways.

As it is given that the number of ways four switches can be set is 2^4 ways.

therefore,

the number of ways four switches can be set

$= 2^4 = 2\times 2\times 2\times 2 =16\ ways$

Statement 2,

A panel of five light switches can be set in twice this many ways.

According to the given information,

the number of ways five switches can be set

= 2 x number of ways four switches can be set

$= 2\times 2^4 \\ = 2\times 2\times 2\times 2\times 2 =32\ ways$

Hence, the number of ways five switches can be set is 32.

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