Question

out of 60 applicants to a university 40 are from south, if 20 applicants are selected at random find the probability that 10 are from south

Answer 1

Variations to choose 20 applicants from 60 is ${60 \choose 20}=\frac {60!} {20!40!}$ Variations to choose 10 applicants from 40 from south is ${40 \choose 10}=\frac {40!} {10!30!}$, variatons to choose 10 applicants from 20 not from south is ${20 \choose 10}=\frac {20!} {10!10!}$

Means probability that from 20 applicants 10 from south is

$/\frac {{40 \choose 10}{20 \choose 10}} {{60 \choose 20}}=\frac {40!20!40!20!} {10!30!10!10!60!}=0.0373$ or 3.73%