A website sells custom messenger bags in 4 sizes. For each size, there are 52 co

Question

A website sells custom messenger bags in 4 sizes. For each size, there are 52 color/fabric combinations. Any of these 52 can be chosen for the left, center, and right panel. In addition, there are 17 different choices of binding color, 26 choices of logo color, 12 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?

Explanation / Answer

Please note nCr = n! / [(n-r)!*r!]. Also some standard formulae are as below.

(i) nCr = nCn-r eg 5C2 = 5C3

(ii) nC1 = n eg 5C1 = 5

We can choose a size in 4C1 = 4 ways

For each size we have a choice of 52 color/Fabric. We can choose 1 in 52C1 = 52 ways

Also Any of these 52 can be chosen for each of left, center and right panel = 52 * 52 * 52

A binding color can be chosen in 17C1 = 17 ways

A logo color can be chosen in 26C1 = 26 ways

A liner color can be chosen in 12C1 = 12 ways

A strap pad color can be chosen in 47C1 = 47 ways

An Interior style can be chosen in 2C1 = 2 ways

We can have 2 choices in either left handed or right handed = 2 ways

We can have 2 choices in with grab strap or without grab strap = 2 ways

We can have 2 choices in with chiller insert or without chiller insert = 2 ways

We can have 2 choices in with camera insert or without camera insert = 2 ways

We can have 2 choices in with water bottle pocket or without water bottle pocket = 2 ways

Therefore Total possible combinations

= 4 * 52 * 52 * 52 * 52 *17 * 26 * 12 * 47 * 2 * 2 * 2 * 2 * 2 * 2 = 4.666 * 1014.

(If rounded to 2 decimal places it is 4.67 * 1014, and if rounded to 1 decimal place it is 4.7 * 1014.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.