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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

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 Dont End Up With A Pen class=

Sagot :

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:

[tex]\text{nCx}=\frac{n!}{x!(n-x)!}[/tex]

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

[tex]8C3=\frac{8!}{3!(8-3)!}=\frac{8!}{3!\cdot5!^{}}=56[/tex]

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:

[tex]4C3=\frac{4!}{3!(4-3)!}=\frac{4!}{3!\cdot1!}=4[/tex]

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

[tex]P=\frac{4}{56}=\frac{1}{14}[/tex]

So, the answer is 1/14

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