Question

a committee of 4 is being formed randomly from the employees at a school: 6 administrators, 38 teachers and 4 staff. what is the probability that all 4 members are administrators? express your answer as a fraction

Answer 1

Answer:

Probability that all 4 memebers are administrators = 1/12972

Step-by-step explanation:

Number of administrators = 6

Number of teachers = 38

Number of staff = 4

Total number of employees in the school = 6 + 38 + 4

Total number of employees in the school = 48

Probability = (Number of possible outcomes) / (Number of total outcomes)

The number of total outcomes is the number of ways of selecting 4 committee members from 48 employess

Number of total outcomes = 48C4

`\begin{gathered} \text{Number of total outcomes = }(48!)/((48-4)!4!) \\ \text{Number of total outcomes = }(48!)/(44!4!) \\ \text{Number of total outcomes = }(48*47*46*45*44!)/(44!4*3*2*1) \\ \text{Number }of\text{ total outcomes = 2}*47*46*45 \\ \text{Number of total outcomes = 19458}0 \end{gathered}`

Number of possible outcomes is the number of ways of selecting 4 committe memebers from 6 administrators

`\begin{gathered} \text{Number of possible outcomes = 6C4} \\ \text{Number of possible outcomes = }(6!)/((6-4)!4!) \\ \text{Number of possible outcomes = }(6!)/(2!4!) \\ \text{NUmber of ossible outcomes = }(6*5*4!)/(2*1*4!) \\ \text{Number of possible outcomes = 3 }*\text{ 5} \\ \text{Number of possible outcomes = 15} \end{gathered}`

Probability that all 4 memebers are administrators = 15/194580

Probability that all 4 memebers are administrators = 1/12972