Matt and some of his friends are going rock climbing this weekend. In preparation, Matt purchased 8 sports drinks to bring, including 6 strawberry flavored drinks. If Matt randomly chooses to place 5 drinks in the red cooler, what is the probability that all of them are strawberry flavored? Write your answer as a decimal rounded to four decimal places. ____

Calculate Probability of First Drink: There are 6 strawberry flavored drinks out of 8 total drinks. To find the probability that the first drink is strawberry flavored, we calculate 6/8.Calculate Probability of Second Drink: If the first drink is strawberry, there are now 5 strawberry drinks left out of 7 total drinks. The probability that the second drink is also strawberry flavored is 5/7.Calculate Probability of Third Drink: Continuing this pattern, the probability for the third drink is 4/6, which simplifies to 2/3.Calculate Probability of Fourth Drink: For the fourth drink, the probability is 3/5.Calculate Probability of Fifth Drink: Finally, the probability for the fifth drink is 2/4, which simplifies to 1/2.Calculate Overall Probability: To find the overall probability that all 5 drinks are strawberry flavored, we multiply the individual probabilities together. So, we calculate (6/8) * (5/7) * (2/3) * (3/5) * (1/2).Perform Multiplication: Performing the multiplication gives us (6/8) * (5/7) * (2/3) * (3/5) * (1/2) = (6*5*2*3*1) / (8*7*3*5*2) = 180 / 1680.Simplify Fraction: Simplify the fraction 180/1680 to get 3/28.

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Matt and some of his friends are going rock climbing this weekend. In preparation, Matt purchased $8$ sports drinks to bring, including $6$ strawberry flavored drinks. $\newline$ If Matt randomly chooses to place $5$ drinks in the red cooler, what is the probability that all of them are strawberry flavored? $\newline$ Write your answer as a decimal rounded to four decimal places. $\newline$ ____ $\newline$

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Precalculus

Find probabilities using combinations and permutations

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Q. Matt and some of his friends are going rock climbing this weekend. In preparation, Matt purchased

8

sports drinks to bring, including

6

strawberry flavored drinks.

\newline

If Matt randomly chooses to place

5

drinks in the red cooler, what is the probability that all of them are strawberry flavored?

\newline

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

\newline

____

\newline

Calculate Probability of First Drink: There are $6$ strawberry flavored drinks out of $8$ total drinks. $\newline$ To find the probability that the first drink is strawberry flavored, we calculate $\frac{6}{8}$ .
Calculate Probability of Second Drink: If the first drink is strawberry, there are now $5$ strawberry drinks left out of $7$ total drinks. $\newline$ The probability that the second drink is also strawberry flavored is $\frac{5}{7}$ .
Calculate Probability of Third Drink: Continuing this pattern, the probability for the third drink is $\frac{4}{6}$ , which simplifies to $\frac{2}{3}$ .
Calculate Probability of Fourth Drink: For the fourth drink, the probability is $\frac{3}{5}$ .
Calculate Probability of Fifth Drink: Finally, the probability for the fifth drink is $\frac{2}{4}$ , which simplifies to $\frac{1}{2}$ .
Calculate Overall Probability: To find the overall probability that all $5$ drinks are strawberry flavored, we multiply the individual probabilities together. $\newline$ So, we calculate $(\frac{6}{8}) \times (\frac{5}{7}) \times (\frac{2}{3}) \times (\frac{3}{5}) \times (\frac{1}{2})$ .
Perform Multiplication: Performing the multiplication gives us $(\frac{6}{8}) \times (\frac{5}{7}) \times (\frac{2}{3}) \times (\frac{3}{5}) \times (\frac{1}{2}) = \frac{6\times5\times2\times3\times1}{8\times7\times3\times5\times2} = \frac{180}{1680}$ .
Simplify Fraction: Simplify the fraction $\frac{180}{1680}$ to get $\frac{3}{28}$ .