Question

Of 24 employees at a local supermarket, 13 work as cashiers and 11 stock shelves. If 4 employees are selected at random to work overtime, determine the probability that all 4 are cashiers.

Answer 1

Answer:

The required probability is, $\simeq 0.06729$

Step-by-step explanation:

Of 24 employees at a local supermarket, 13 work as cashiers  and 11 stock shelves. If 4 employees are selected at random to work overtime, then

P( all 4 are cashiers) = $\frac{^{13}{C}_{4}}{^{24}{C}_{4}}$

                                 $\simeq 0.06729$

Answer 2

Answer:  $\dfrac{65}{996}$

Step-by-step explanation:

Given : Total number of employees = 24

Number of cashiers = 13

Number of stock shelves = 11

Number of ways to choose 4 out of 24 people = $^{24}C_4$  (Total outcomes)

Number of ways to select 4 out of 13 cashiers = $^{13}C_{4}$ (Favorable outcomes)

According to the definition of probability : $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

Then , the probability that all selected 4  employees are cashiers. :-

$\dfrac{^{13}C_4}{^{24}C_{4}}\\\\=\dfrac{\dfrac{13!}{4!9!}}{\dfrac{24!}{4!20!}}\\\\=\dfrac{65}{996}$

Hence, the required probability is $\dfrac{65}{996}$ .