Question

A website sells custom messenger bags in 4 sizes. For each​ size, there are 53 ​color/fabric combinations. Any of these 53 can be chosen for the​ left, center, and right panel. In​ addition, there are 18 different choices of binding​ color, 27 choices of logo​ color, 12 choices of liner​ color, and 47choices 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

1 bag can be chosen out of 4 = 4 ways

The left panel can have 1 color out of 53 in 53 ways

The right panel can have 1 color out of 53 in 53 ways

The center panel can have 1 color out of 53 in 53 ways

1 binding color can be chosen out of 18 in 18 ways

1 logo color can be chosen out of 27 in 27 ways

1 liner color can be chosen out of 12 in 12 ways

1 strap pad color can be chosen out of 47 in 47 ways

1 interior choice can be chosen out of 2 in 2 ways

1 choice out of 2 for left handed or right handed in 2 ways

1 choice out of 2 for grab strap or no grab strap in 2 ways

1 choice out of 2 for chiller insert or no chiller insert in 2 ways

1 choice out of 2 for camera insert or no camera insert in 2 ways

1 choice out of 2 for water bottle pocket or no water bottle pocket in 2 ways

hence,

Total possible combinations=4*53*53*53*18*27*12*47*2*2*2*2*2*2=10446791989248

=1.045 X 10¹³