Answer to Question #109150 in Statistics and Probability for Syamimi

Question

Four of the Statistics for Business and Economics students submitted an entry to a Math contest at the faculty. A total of 24 entries were submitted. Six of the entries will move on to the next round.
a. What is the hypergeometric probability that all four Statistics for Business and Economics students will move on to the next round? (2 Marks)

Answer 1

$P=\frac{C_6^4\cdot C_{18}^2}{C_{24}^6}\approx 0.017.$

We choose 6 entries. 4 of them should belong to each of four students. Then we choose 2 more entries of 18.