5 students are randomly seated along the side of a table. What is the probability that they are seated in order of age?
What is 5! ?
5!=120
1/120= 0.0083
but the options are
0.1
0.054
0.0167
Impossible to determine
Am I missing something?
You are missing the fact that they could be ordered according to increasing or according to decreasing age.
Each would be ordered by age.
so prob = 2/120 = 1/60 = appr .0167
Ah okay. Thanks!
To find the probability that the students are seated in order of age, we need to calculate the total number of possible seating arrangements and the number of arrangements where the students are seated in order of age.
Step 1: Calculate the total number of possible seating arrangements:
Since there are 5 students, there are 5! (read as 5 factorial) ways to arrange them along the side of the table.
5! = 5 x 4 x 3 x 2 x 1 = 120
Step 2: Calculate the number of arrangements where the students are seated in order of age:
When the students are seated in order of age, the youngest student must occupy the leftmost seat, and the oldest student must occupy the rightmost seat. The remaining students can be seated in any order between them.
Since the youngest student has already been assigned the leftmost seat, we only need to calculate the number of arrangements for the other 4 students.
For the remaining 4 students, there are 4! ways to arrange them.
4! = 4 x 3 x 2 x 1 = 24
Step 3: Calculate the probability:
To find the probability, we divide the number of arrangements where the students are seated in order of age by the total number of possible seating arrangements.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 24 / 120
Probability = 1/5
Probability = 0.2 or 20%
Therefore, the probability that the 5 students are seated in order of age is 0.2 or 20%.