A juice company decides to test five different brands of juice. The different brands have been labeled A B C D and E the company, decides to compare each brand with the other brands by comparing together different brands. How many different pairs will result by selecting two different brands at a time?
There will be 10 different pairs resulting from selecting two different brands at a time.
To find the number of different pairs that result from selecting two different brands at a time, you can use a combination formula.
Since there are five different brands (A, B, C, D, E), you need to select 2 brands at a time. The number of combinations of selecting 2 brands out of 5 can be calculated using the combination formula:
C(n, r) = n! / ((n-r)! * r!)
Here, n is the total number of items (brands) and r is the number of items to be selected (2 in this case). For this specific problem, it would be:
C(5, 2) = 5! / ((5-2)! * 2!)
Let's break down the calculation:
5! = 5 * 4 * 3 * 2 * 1 = 120
(5-2)! = 3! = 3 * 2 * 1 = 6
2! = 2 * 1 = 2
Now, we can substitute these values back into the formula:
C(5, 2) = 120 / (6 * 2) = 120 / 12 = 10
Therefore, there would be 10 different pairs that result from selecting two different brands at a time.
To find the number of different pairs that can be formed by selecting two different brands at a time, we can use the combination formula.
The formula for calculating the number of combinations is given by:
C(n, r) = n! / (r!(n-r)!)
In this case, n represents the total number of brands, which is 5, and r represents the number of brands we want to select at a time, which is 2.
Plugging in the values into the equation, we have:
C(5, 2) = 5! / (2!(5-2)!)
= 5! / (2!3!)
= (5 * 4 * 3!) / (2! * 3!)
= (5 * 4) / 2
= 10
Therefore, there will be 10 different pairs that can be formed by comparing two different brands at a time.