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Mr. Lynch brought in $8$ solid colored eggs for his Physics classes. $6$ of the eggs were green. If Mr. Lynch randomly chose $5$ eggs for his first class to use in an egg drop experiment, what is the probability that all of them are green? $\newline$ Write your answer as a decimal rounded to four decimal places.._________

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Find probabilities using combinations and permutations

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Q. Mr. Lynch brought in

8

solid colored eggs for his Physics classes.

6

of the eggs were green. If Mr. Lynch randomly chose

5

eggs for his first class to use in an egg drop experiment, what is the probability that all of them are green?

\newline

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

Total Eggs Selection Calculation: Total number of eggs: $8$ $\newline$ Eggs to choose for the experiment: $5$ $\newline$ Calculate total possible outcomes using combinations. $\newline$ Total outcomes: $\binom{8}{5}$
Total Possible Outcomes Calculation: Find the value of $\binom{8}{5}$ . $\newline$ $\binom{8}{5} = \frac{8!}{5!(8-5)!} = \frac{8!}{5!3!} = \frac{8 \times 7 \times 6 \times 5!}{5! \times 3 \times 2 \times 1} = 56$
Green Eggs Selection Calculation: Number of green eggs: $6$ $\newline$ Number of chosen green eggs: $5$ $\newline$ Calculate favorable outcomes using combinations. $\newline$ Favorable outcomes: $_{6}C_{5}$
Probability Calculation: Find the value of $\binom{6}{5}$ . $\binom{6}{5} = \frac{6!}{5!(6-5)!} = \frac{6!}{5!1!} = \frac{6 \times 5!}{5! \times 1} = 6$
Probability Calculation: Find the value of $\binom{6}{5}$ . $\newline$ $\binom{6}{5} = \frac{6!}{5!(6-5)!}$ $\newline$ $= \frac{6!}{5!1!}$ $\newline$ $= \frac{6 \times 5!}{5! \times 1}$ $\newline$ $= 6$ Calculate the probability that all chosen eggs are green. $\newline$ Probability = Favorable outcomes / Total possible outcomes $\newline$ $= \frac{6}{56}$ $\newline$ $\approx 0.1071$

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