Answer to Question #96168 in Statistics and Probability for Durvesh gaonkar

Question

There are 30 tickets numbered 1 to 30 in a box 5 tickets are drawn at random & arranged in ascending order of magnitude .what is the probability that middle tickets equal to 10.

Answer 1

Since the middle ticket equals to 10, there should be two numbers smaller than 10 and two numbers greater than 10.

The number of ways to draw 2 numbers from 9 (numbers smaller than 10) is $\binom{9}{2}$, the number of ways to draw 2 numbers from 20 (numbers greater than 10) is $\binom{20}{2}$.

The number of ways to draw 5 numbers from 30 numbers is $\binom{30}{5}$.

Probability that middle tickets equal to 10 is $\frac{}{}$ $\frac{\binom{9}{2}\cdot\binom{20}{2}}{\binom{30}{5}}=$

$\frac{1\cdot2\cdot3\cdot4\cdot5\cdot9\cdot8\cdot20\cdot19}{30\cdot29\cdot28\cdot27\cdot26\cdot2\cdot2}=\frac{380}{7917}\approx0.048.$

Answer: 0.048.