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Brenna is handing out $8$ invitations to her New Year's Eve party, $5$ of which are printed on green paper. If Brenna randomly hands out $4$ invitations before lunch, what is the probability that all of them are printed on green paper? $\newline$ Write your answer as a decimal rounded to four decimal places.._________

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Find probabilities using combinations and permutations

Full solution

Q. Brenna is handing out

8

invitations to her New Year's Eve party,

5

of which are printed on green paper. If Brenna randomly hands out

4

invitations before lunch, what is the probability that all of them are printed on green paper?

\newline

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

Total Invitations Count: Total invitations: $8$ $\newline$ Green invitations: $5$ $\newline$ Invitations to hand out before lunch: $4$ $\newline$ Calculate total possible combinations of handing out $4$ invitations from $8$ . $\newline$ \substack{8\C_4} = \frac{8!}{4!(8-4)!}
Green Invitations Count: ${}_8C_4 = \frac{8!}{4!4!}$ $= \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1}$ $= 70$
Invitations Before Lunch: Calculate combinations of handing out $4$ green invitations from $5$ .
_$5$C_$4$ = $(5!) / (4!(5-4)!)$
Calculate Total Combinations: ${}_5C_4 = \frac{5!}{4!1!}$ = $\frac{5 \times 4!}{4! \times 1}$ = $5$
Calculate Combinations of Green Invitations: Calculate the probability. $\newline$ Probability = Favorable outcomes / Total possible outcomes $\newline$ = $\frac{5}{70}$
Calculate Probability: Convert to decimal and round to four decimal places. $\newline$ Probability $\approx 0.0714$

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