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?
Questions A, B, C, D, E, F, G, H
AB, AC, AD, AE, AF, AG, AH
BC, BD, BE, BF, BG, BH
Take it from there.
8 choose 2=8!/6!2!=8x7/2=28
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To find the number of different groups of 2 essays that you could possibly choose from the 8 options, you need to use a combination formula. The formula to calculate the number of combinations is:
C(n, r) = n! / (r!(n-r)!)
Where:
- n represents the total number of items
- r represents the number of items chosen
In this case, you have 8 essays to choose from and you need to choose 2 essays. So, you can plug in these values into the formula:
C(8, 2) = 8! / (2!(8-2)!)
First, calculate the factorial of 8 (8!) which is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40,320.
Next, calculate the factorial of 2 (2!) which is 2 x 1 = 2.
Finally, calculate the factorial of (8-2) which is 6 x 5 x 4 x 3 x 2 x 1 = 720.
Now, plug these values into the combination formula:
C(8, 2) = 40,320 / (2 x 720)
= 40,320 / 1,440
= 28
Therefore, you could possibly choose from 28 different groups of 2 essays out of the 8 options.