Complete Question
In a small private school, 5 students are randomly selected from 13 available students. What is the probability that they are the five youngest students?
Answer:
The probability is [tex]P(x) = 0.00078[/tex]
Step-by-step explanation:
From the question we are told that
The number of student randomly selected is r = 5
The number of available students is n = 13
Generally the number of ways that 5 students can be selected from 13 available students is mathematically represented as
[tex]n(k)=\left n} \atop {}} \right.C_r = \frac{n ! }{(n-r ) ! r!}[/tex]
substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{13 ! }{(13-5 ) ! 5!}[/tex]
[tex]\left n} \atop {}} \right.C_r = \frac{13 * 12 * 11 * 10 * 9 *8! }{8 ! * 5 * 4 * 3 * 2 *1}[/tex]
[tex]\left n} \atop {}} \right.C_r = 1287[/tex]
The number of method by which 5 youngest students are selected is n(x) = 1
So
Then the probability of selecting the five youngest students is mathematically represented as
[tex]P(x) = \frac{n(x)}{n(k)}[/tex]
substituting values
[tex]P(x) = \frac{1}{1287}[/tex]
[tex]P(x) = 0.00078[/tex]
