Alocal t-shirt company has 20 slogans for the front of the shirt, 50 colors of shirts, 15 logos for the back of the shirt, and 10 shirt sizes. in how many ways can a shirt be created, if one option is selected for each category? 100,000 150,000 200,000 250,000

In 150000 ways a shirt be created, if one option is selected for each of given category.

Solution:

Given that  

A local T-shirt company has  20 slogans for the front of the shirt,  50 colors of shirts,  15 logos for the back of the shirt , 10 shirt size

Need to determine in how many ways can a shirt be created , if one option is selected from each category.

Number of ways in which t – shirt from 20 slogans can be created = 20

Number of ways 1 colour t-shirt  from 20 slogans can be created = 20 x 1

So number of ways 50 colour t shirts from 20 slogas can be created = 20 x 50

Extending the same idea of multiplication for each option we can say that Number of ways in which T shirts from 20 slogans , 50 colors , 15 logos  , 10 shirt sie can be created =

Hence in 150000 ways a shirt be created, if one option is selected for each of given category.