Using the concept of probability and the arrangements formula, there is a
0.002 = 0.2% probability that the first 8 people in line are teachers.
----------------------------------
- A probability is the number of desired outcomes divided by the number of total outcomes.
- The order in which they are positioned is important, and all people will be positioned, and thus, the arrangements formula is used to find the number of outcomes.
The number of possible arrangements from a set of n elements is given by:
[tex]A_n = n![/tex]
----------------------------------
The desired outcomes are:
- First 8 people are teachers, in 8! possible ways.
- Last 4 are students, in 4! possible ways.
Thus, [tex]D = 8! \times 4![/tex]
----------------------------------
For the total outcomes, number of arrangements of 12 people, thus:
[tex]T = 12![/tex]
The probability is:
[tex]p = \frac{D}{T} = \frac{8! \times 4!}{12!} = 0.002[/tex]
0.002 = 0.2% probability that the first 8 people in line are teachers.
A similar problem is given at https://brainly.com/question/24650047
