Question

A street sign can be ordered with the following options:

Sheeting: Option A or Option B
Power Type: Option A or Option B
Timer: Option A, Option B or Option C
Push Button: Option A, Option B or Option C
Channel: Option A, Option B or Option C
Sensor: Option A, Option B or Option C

How many total configurations are there?

Answer 1

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Answer on Question #49216 – Math – Combinatorics | Number Theory

A street sign can be ordered with the following options:

- Sheeting: Option A or Option B

- Power Type: Option A or Option B

- Timer: Option A, Option B or Option C

- Push Button: Option A, Option B or Option C

- Channel: Option A, Option B or Option C

- Sensor: Option A, Option B or Option C

How many total configurations are there?

Solution

A street sign can be ordered with the following options:

- Sheeting: Option A or Option B – 2 states

- Power Type: Option A or Option B – 2 states

- Timer: Option A, Option B or Option C – 3 states

- Push Button: Option A, Option B or Option C – 3 states

- Channel: Option A, Option B or Option C – 3 states

- Sensor: Option A, Option B or Option C – 3 states

Consider options within arbitrary category are independent of options from other categories. Hence, by multiplication rule, total number of configurations is just a product of numbers of distinct categories' states.

$$2 * 2 * 3 * 3 * 3 * 3 = 2 ^ {2} * 3 ^ {4} = 4 * 8 1 = 3 2 4$$

Answer: 324