Question

In a small private​ school, 55 students are randomly selected from 1313 available students. What is the probability that they are the fivefive youngest​ students?

Answer 1

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
`P(x) = 0.00078`

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

`n(k)=\left n} \atop {}} \right.C_r = (n ! )/((n-r ) ! r!)`

substituting values

`\left n} \atop {}} \right.C_r = (13 ! )/((13-5 ) ! 5!)`

`\left n} \atop {}} \right.C_r = (13 * 12 * 11 * 10 * 9 *8! )/(8 ! * 5 * 4 * 3 * 2 *1)`

`\left n} \atop {}} \right.C_r = 1287`

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

`P(x) = (n(x))/(n(k))`

substituting values

`P(x) = (1)/(1287)`

`P(x) = 0.00078`