IXL - Find probabilities using combinations and permutations (Algebra 2 practice)

A company is hosting a welcome lunch for all 9 of their recently hired employees, including 7 from the finance department. The company wants the employees to intermingle, and not just socialize with their own department.

If the event organizer randomly selected 6 of the new employees to sit at a table together, what is the probability that all of them are from the finance department?

Write your answer as a decimal rounded to four decimal places.

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Learn with an example

question

Simon has a collection of 9 dice, 7 of which have four sides.

If Simon randomly rolls 6 dice, what is the probability that all of them have four sides?

Write your answer as a decimal rounded to four decimal places.

key idea

A uniform probability model is a sample space in which all outcomes are equally likely.

In a uniform probability model, the probability of an event

is the number of outcomes in that event divided by the total number of outcomes in the sample space:

(

)

# of outcomes in

total # of outcomes

A factorial is a whole number followed by an exclamation point. The value of

is 1, and for a positive integer

(

–

)

The number of ways to choose

different objects from a set of

objects is

(

–

)

solution

To find the probability that all 6 dice have four sides, first identify the sample space and the event.

The sample space consists of outcomes that are ways to choose 6 dice from the set of 9 dice. In other words, each outcome is a subset of 6 dice. Each subset is equally likely, so this is a uniform probability model.

The event is that all 6 dice have four sides.

Since this is a uniform probability model, count the number of outcomes in the event and count the total number of outcomes, then divide them to compute the probability.

Count the total number of outcomes.

Each outcome in the sample space is a subset of 6 dice chosen from the set of 9 dice. So, the total number of outcomes is the number of ways to choose 6 dice from the set of 9, which is

total # of outcomes

Count the number of outcomes in the event.

Count the number of outcomes in which all 6 dice have four sides. There are

ways to choose 6 dice from the set of 7 dice that have four sides.

# of outcomes in the event

Find the probability.

The probability that all 6 dice have four sides is

≈

0.0833

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Teacher tools

Work it out

Not feeling ready yet? These can help:

OO.3Combinations and permutations

JJ.1Probability of simple events

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