Respuesta :
To solve the problem we must know about Permutation and Combination.
The number of different types of shirts available from this company is 42.
Given to us
- A shirt company has 3 designs each of which can be made with short or long sleeves.
- There are 7 color patterns available.
As given to us there are 3 designs available,
- Number of designs = [tex]^3C_1[/tex],
- Number of ways the sleeves can be made = [tex]^2C_1[/tex] (short or long sleeves),
- Number of color patterns available = [tex]^7C_1[/tex]
Total number of ways in which a shirt can be made
Total number of ways in which a shirt can be made [tex]= ^3C_1\times ^2C_1\times ^7C_1[/tex]
= 3 x 2 x 7
= 42 ways
Hence, the number of different types of shirts available from this company is 42.
Learn more about Permutation and Combination:
https://brainly.com/question/11732255
