Five students are randomly selecting polygons and we are asked to find the probability that the first two students choose the triangle and the quadrilateral, in that order.

To do that we will compare the number of

favorable

o u t c o m e s

with the number of

possible

o u t c o m e s .

P = \frac{Favorable outcomes}{Possible outcomes}

First let's find the number of

possible

outcomes,

which is the number of all the possible selections of the polygons.

The number of the possible selections of the polygons is equal to the number of permutations of

5

polygons, which is

5! .

Possible outcomes = 5!

The favorable outcomes are the possible selections of the polygons where the first two student choose the triangle and quadrilateral in that order. This means that the last three students can choose the pentagon, the hexagon, or the octagon.

Therefore, the number of favorable outcomes is the number of permutations of

3

polygons, which is

3! .

Favorable outcomes = 3!

Finally, we can substitute the numbers of

favorable

outcomes

and

possible

outcomes

into the formula for the probability that the first two students choose the triangle and the quadrilateral.

P = \frac{Favorable outcomes}{Possible outcomes} = \frac{3 !}{5 !}

Let's calculate the probability!

P = \frac{3 !}{5 !}

Write as a product

P = \frac{3 !}{5 \cdot 4 \cdot 3 !}

CancelCommonFac

Cancel out common factors

P = \frac{3 !}{5 \cdot 4 \cdot 3 !}

SimpQuot

Simplify quotient

P = \frac{1}{5 \cdot 4}

Multiply

P = \frac{1}{2 0}

We found that the probability is

\frac{1}{2 0} .

Exercise

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