Question

In a small private​ school, 5 students are randomly selected from 14 available students. What is the probability that they are the five youngest​ students?

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

$\frac{1}{2002}$ or $0.0004995$

Step-by-step explanation:

Total students$= 14$  

No of the students chosen$= 5$  

The group of these students matters and not the order of selecting them. Hence, we'll find the total number of combinations.

Possible combinations =$\frac{14!}{9!*5!}$=$\frac{14*13*12*11*10*9!}{9!*5!}$=$\frac{14*13*12*11*10}{5*4*3*2*1}$=$2002$

No of possible favorable options for all $5$ being the youngest students $= 1$

As there is only one possible combination where all five youngest are chosen.

Hence,

The probability of all five are youngest students getting selected will be

$=\frac{1}{2002}$$=0.0004995$