Answer to Question #297772 in Statistics and Probability for kool

Question

Pramod goes to a shop to buy some clothes. Shopkeeper shows him 5 shirts, 6 pants and 13 t-shirts. If he selects three clothes at random, then find the probability that, randomly chosen clothes does not contain pant.

Answer 1

There are $5+6+13=24$ clothes. Pramod can select three clothes in $\dbinom{24}{3}=2024.$

Then

$$P(No\ pants)=\dfrac{\dbinom{5+13}{3}\dbinom{6}{0}}{\dbinom{24}{3}}=\dfrac{816(1)}{2024}$$

$$=\dfrac{102}{253}$$

The probability that, randomly chosen clothes does not contain pant is $\dfrac{102}{253}\approx0.403.$