A juice company decides to test six different brands of juice by comparing each brand with each of the other brands. How many different pairs of the six juices will be tested?
10
12
15
7
is it 15?
15
correct
Well, let's put our thinking caps on and calculate it together! If we have six different brands of juice, we can pair each one with the other five. To find the total number of pairs, we use the formula n(n-1)/2 where n is the number of elements. So, in this case, we have 6(6-1)/2 = 6(5)/2 = 30/2 = 15. So, you're absolutely right, it's 15! Give yourself a high five or, better yet, treat yourself to a nice glass of juice!
To determine the number of different pairs of the six juices that will be tested, you can use a combination formula. The formula for finding the number of combinations of n items taken k at a time is:
C(n, k) = n! / (k! * (n - k)!)
In this case, you want to find the number of combinations when selecting 2 juices at a time from a total of 6 juices. Plugging the values into the formula:
C(6, 2) = 6! / (2! * (6 - 2)!)
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / (2 * 1)
= 15
Therefore, the correct answer is 15.
Yes, you are correct. The number of different pairs of the six juices that will be tested can be determined using the formula for combinations. In this case, we can calculate it using the formula:
nCr = n! / (r! * (n - r)!)
Where n represents the total number of items and r represents the number of items to be chosen at a time.
In this scenario, there are six different brands of juice to be tested. To determine the number of pairs, we need to choose 2 items at a time from the 6 items.
So, we can calculate it as:
6C2 = 6! / (2! * (6 - 2)!)
= 6! / (2! * 4!)
= (6 * 5 * 4!) / (2! * 4!)
= (6 * 5) / (2 * 1)
= 30 / 2
= 15
Therefore, there will be 15 different pairs of the six juices tested.