Respuesta :
Answer:
The different card designs possible are:
224
Step-by-step explanation:
It is given that:
There are 2 sizes, 4 colors, 7 phrases, and 4 pictures for her to choose from. (The printing company charges a fee to add extra design elements, so she will choose only one of each.)
As she has to choose one from each given item this means she will use a combination to choose the item.
We know that the combination for r choices out of total n choices is given as:
[tex]n_C_r=\dfrac{n!}{r!\times (n-r)!}[/tex]
Hence, the total combinations made are given as:
[tex]2_C_1\times 4_C_1\times 7_C_1\times 4_C_1\\\\\\=\dfrac{2!}{1!\times (2-1)!}\times \dfrac{4!}{1!\times (4-1)!}\times \dfrac{7!}{1!\times (7-1)!}\times \dfrac{4!}{1!\times (4-1)!}\\\\=2\times 4\times 7\times 4\\\\=224[/tex]
Hence, the different card designs that are possible are:
224
The different card designs that are possible will be 224. The formula for the combination is used to solve the problem.
What are permutation and combination?
A permutation is an act of arranging the objects or elements in order.
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
The given data in the problem is;
Paula is going to choose 2 sizes, 4 colors, 7 phrases, and 4 pictures . If the one item has to be chosen;
The total combination is;
[tex]= \rm 2C_1 \times 4C_1 \times 7C_1 \times 4 C_1 \\\\ = \frac{2!}{1!\times (2-1)!} \times \frac{4!}{1! \times (4-1)!} \times \frac{7!}{1!\times (7-1)!} \times \frac{4!}{1!\times (4-1)!} \\\\ =2 \times 4 \times 7 \times 4 \\\\ =224[/tex]
Hence different card designs are possible will be 224.
To learn more about the permutation and combination refer;
https://brainly.com/question/13387529
#SPJ3
