Question

A cola company decides to test five different brands of soft drink. The different brands have been labeled F, G, H, I, and J. The company decides to compare each brand with the other brands by pairing them together. How many different pairs will result from selecting two different brands at a time?
A) 25

B) 20

C) 12

D) 10


PLEASEEE HELPPP!!!!!!!!!!!!!!!!

Answer 1

The answer is B) 20

Because you have 5 brands and you combine each with the 4 others, so 5*4=20

Answer 2

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:

$nCk=\frac{n!}{k!(n-k)!}$

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:

$5C2=\frac{5!}{2!(5-2)!}$

$5C2= \frac{5*4*3*2*1}{(2*1)*(3**2*1)} =\frac{120}{12} =10$

Then, we can form 10 different pairs of brands with a group of 5 different brands.