Question

A website sells custom messenger bags in 5 sizes. For each​ size, there are 54 ​color/fabric combinations. Any of these 54 can be chosen for the​ left, center, and right panel. In​ addition, there are 17 different choices of binding​ color, 28 choices of logo​ color, 11 choices of liner​ color, and 47 choices of strap pad color. There are 2 choices for the interior style. The bag can be​ right- or​ left-handed. It can be ordered with or without a grab​ strap, a chiller​ insert, a camera​ insert, and a water bottle pocket. How many different bags are​ possible?

Answer 1

60

Explanation:

Answer 2

There are 1,066,055,680 different possible bags.

The Breakdown

To calculate the total number of different bags that are possible, we need to multiply the number of choices for each customizable feature.

Given the following choices:

- 5 sizes

- 54 color/fabric combinations for each size

- 54 choices for the left panel color/fabric

- 54 choices for the center panel color/fabric

- 54 choices for the right panel color/fabric

- 17 choices for binding color

- 28 choices for logo color

- 11 choices for liner color

- 47 choices for strap pad color

- 2 choices for interior style

- 2 choices for right- or left-handed

- 2 choices for grab strap (with or without)

- 2 choices for chiller insert (with or without)

- 2 choices for camera insert (with or without)

- 2 choices for water bottle pocket (with or without)

To calculate the total number of different bags, we multiply all of these choices together:

5 × 54 × 54 × 54 × 17 × 28 × 11 × 47 × 2 × 2 × 2 × 2 × 2 = 1,066,055,680

Therefore, there are 1,066,055,680 different possible bags.