Paula is going to choose the size, color, phrase, and picture for a birthday card for her friend. 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.) How many different card designs are possible?

Answer:The different card designs possible are:224Step-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