Answer:
D) 10
Step-by-step explanation:
For calculate the number of ways in which we can form pairs, we need to use the following equation:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
Where nCk give as the number of ways in which we can form groups of k elements from a group of n element.
In this case we have 5 different brands and we need to conform groups of 2.
So, In this case n is equal to 5 and k is equal to 2, replacing this values on the equation of nCk, we get:
[tex]5C2=\frac{5!}{2!(5-2)!}[/tex]
[tex]5C2= \frac{5*4*3*2*1}{(2*1)*(3**2*1)} =\frac{120}{12} =10[/tex]
Then, we can form 10 different pairs of brands with a group of 5 different brands.
