Question

Ten people apply for a job as assistant manager of a restaurant. Five have completed college and five have not. If the manager selects 3 applicants at random, find the probability that all 3 are college graduates.

Answer 1

it is given that total number of people (n) = 10

number of selection is r = 3

number of pople who are graduates = 5 and who are not graduates = 5

Using combination formula

Number of ways of selecting 3 out of 10 = C(10,3)

= 10!/((10-3)!*3!)

= 10!/(7!*3!)

= (10*9*8)/(3*2*1) ..............................................10! is written as 10*9*8*7!, then 7! will be cancelled out from numerator and denominator

= 120 ways

Number of ways to select 3 out of 5 college graduates = C(5,3)

= 5!/((5-3)!*3!)

= 5!/(2!*3!)

= (5*4)/(2*1) ..............................................5! is written as 10*4*3!, then 3! will be cancelled out from numerator and denominator

= 10 ways

Therefore, required probability = (number of ways of selecting 3 out of 5)/(number of ways of selecting 3 out of 10)

= 10/120

= 1/12 or 0.0833