Answer to Question #223513 in Statistics and Probability for Kbk

Question

Suppose we have a group of 50 TV’s and decide to sample 15. What is the probability that the 15 selected contain the best 5 TV’s? 

Answer 1

It follows that the probability $p$ that the 15 selected contain the best 5 TV’s is equal to

$p=\dfrac{{50 \choose 5}}{{50 \choose 15}}=\dfrac{\frac{50!}{5!45!}}{\frac{50!}{15!35!}}=\dfrac{15!35!}{5!45!} =\dfrac{15\cdot 14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6}{45\cdot 44\cdot 43\cdot 42\cdot 41\cdot 40\cdot 39\cdot 38\cdot 37\cdot 36}$

$=\dfrac{ 7}{ 43\cdot 41\cdot 38\cdot 37\cdot 3}=\dfrac{7}{7436334}.$