Question

A club with

45

college students is doing volunteer work this semester. Each student is volunteering at one of four locations. Here is a summary.

Location	Number of students
Soup kitchen	18
Hospital	13
Nursing home	4
Pet shelter	10

Three students from the club are selected at random, one at a time without replacement. What is the probability that none of the three students volunteer at the nursing home?

Do not round your intermediate computations. Round your final answer to three decimal places.

Answer 1

As we are doing the selections without replacement here, the probability that none of the three student volunteers selected are from the nursing home is computed here as:

= Number of ways to select 3 students from the 41 non nursing home location / Number of ways to select 3 students from total of 45 students

$= \frac{\binom{41}{3}}{\binom{45}{3}} = \frac{41*40*39}{45*44*43} = 0.7512$

Therefore 0.751 is the required probability here.