Question

A junk drawer at home contains eight pens four of which work what is the probability that a randomly grab three pens from the drawer and don’t end up with a pen that works express your answer as a fraction in lowest terms or decimal rounded to the nearest million

Answer 1

Answer:

1/14

Explanation:

The number of ways or combinations in which we can select x objects from a group of n can be calculated as:

$\text{nCx}=\frac{n!}{x!(n-x)!}$

So, if we are going to select 3 pens from the drawer that contains 8 pens, the number of possibilities is:

$8C3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!\cdot5!^{}}=56$

Then, if we didn't end up with a pen that works is because we select the three pens from the 4 that didn't work. In this case, the number of possibilities is:

$4C3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=4$

Therefore, the probability required is equal to the ratio of these quantities:

$P=\frac{4}{56}=\frac{1}{14}$

So, the answer is 1/14