How many two-person committees can be selected from a set of 8 people.
8nCr2=28
I need a reason why it is 28 when you input it into the calculator
you are filling two slots ... 8 people for the 1st, and 7 people for the second
... 8 * 7 = 56
BUT ... Joe and Sue on the committee is the same as Sue and Joe
... order is not important
so there are 56/2 ways to select the committee
To calculate the number of two-person committees that can be selected from a set of 8 people, you can use the combination formula, also known as nCr.
The formula for nCr is:
nCr = n! / (r!(n - r)!)
In this case, n represents the total number of options (which is 8, since there are 8 people), and r represents the number of selections (which is 2, since we want to choose two-person committees).
So, plugging in the values into the formula:
8C2 = 8! / (2!(8 - 2)!)
Simplifying this equation:
8! = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40320
2! = 2 × 1 = 2
(8 - 2)! = 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
Now, substituting these values back into the equation:
8C2 = 40320 / (2 × 720)
= 40320 / 1440
= 28
Therefore, there are 28 different two-person committees that can be selected from a set of 8 people.