You have to answer
2
essay questions for an exam. There are
8
essays to choose from. How many different groups of
2
essays could you possibly choose?
To solve this problem, we can use the concept of combinations. Combinations help us determine the number of ways to choose a certain number of items from a larger set without considering the order in which the items are chosen.
In this case, we want to know the number of different groups of 2 essays we can choose from a set of 8 essays.
The formula for combinations is:
nCr = n! / ((n - r)! * r!)
Where n represents the total number of items to choose from, and r represents the number of items we want to choose. The exclamation point (!) denotes factorial.
Plugging in the values for our problem:
n = 8 (total number of essays)
r = 2 (number of essays we want to choose)
We get:
8C2 = 8! / ((8 - 2)! * 2!)
Simplifying further:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320
(8 - 2)! = 6! = 6 * 5 * 4 * 3 * 2 * 1 = 720
2! = 2 * 1 = 2
8C2 = 40320 / (720 * 2) = 40320 / 1440 = 28
Therefore, there are 28 different groups of 2 essays that could be chosen.
21
Let's number each essay, 1 - 8
1, 2; 1,3; 1,4; 1,5; 1,6; 1,7;, 1,8 >> 8
2,3; 2,4; 2,5; 2,6, 2,7; 2,8 >> 6
Keep going.
There are 8 ways to choose the 1st question.
Now that that one's taken, there are 7 ways to choose the 2nd one.
So, ...