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Mr. Shen brought in $8$ solid colored eggs for his Physics classes. $5$ of the eggs were blue. If Mr. Shen randomly chose $4$ eggs for his first class to use in an egg drop experiment, what is the probability that all of them are blue? 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. Shen brought in

8

solid colored eggs for his Physics classes.

5

of the eggs were blue. If Mr. Shen randomly chose

4

eggs for his first class to use in an egg drop experiment, what is the probability that all of them are blue? Write your answer as a decimal rounded to four decimal places.._________

Total eggs calculation: Total eggs: $8$ $\newline$ Blue eggs: $5$ $\newline$ Eggs to choose: $4$ $\newline$ Calculate total possible outcomes using combinations.
Total outcomes calculation: Total outcomes: $\binom{8}{4}$
Favorable outcomes calculation: ${}_8C_4 = \frac{8!}{4!(8-4)!} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70$
Probability calculation: Favorable outcomes: $\binom{5}{4}$
Conversion to decimal: _{$\newline$ $5$}C_{$\newline$ $4$} = \(\newline\$\frac{5!}{4!(5-4)!}\)\(\newline\)\) = \(\(\newline\)\$\frac{5 \times 4!}{4! \times 1}\)\(\newline\)\) = \(\(\newline\)5\)
Conversion to decimal: \( {}_5C_4 = \frac{5!}{4!(5-4)!} \)\( = \frac{5 \times 4!}{4! \times 1} \)\( = 5 \)Probability = Favorable outcomes / Total possible outcomes\( = \frac{5}{70} \)
Conversion to decimal: _\(5\)C_\(4\) = \(\frac{5!}{4!(5-4)!}\) = \(\frac{5 \times 4!}{4! \times 1}\) = \(5\)Probability = Favorable outcomes / Total possible outcomes = \(\frac{5}{70}\)Convert to decimal and round to four decimal places. = \(0.0714\)

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