Answer to Question #147036 in Statistics and Probability for Tarang

Question

Out of 60 applicants 40 are from south if 20 applicants are selected as random find probability that not more than 2 are from south

Answer 1

The number of ways to choose 20 applicants out of 60 is ${60 \choose 20}=\frac {60!} {20!40!}$. The number of ways to choose 2 applicants out of 40 from south is ${40 \choose 2}=\frac {40!} {2!38!}$, the number of ways to choose 18 applicants out of 20 not from south is ${20 \choose 18}=\frac {20!} {18!2!}$, the number of ways to choose 1 applicant out of 40 from south is ${40 \choose 1}=\frac {40!} {1!39!}$, the number of ways to choose 19 applicants out of 20 not from south is ${20 \choose 19}=\frac {20!} {19!1!}$, the number of ways to choose 0 applicants out of 40 from south is 1, the number of ways to choose 20 applicants out of 20 not from south is 1.

The probability that out of 20 applicants 10 are from south is

$\frac {{40 \choose 2}{20 \choose 18} + {40 \choose 1}{20 \choose 19} + 1*1} {{60 \choose 20}}=\frac {\frac {40!20!} {2!38!2!18!} + \frac {40!20!} {1!39!1!19!} + 1} {\frac {60!} {20!40!}}=3.554*10^{-11}$ or $3.554*10^{-9}$ %