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Erin bought $9$ seeds in order to plant an herb garden for her grandma. Of the seeds she bought, $7$ were dill seeds. $\newline$ If Erin chooses to plant $6$ random seeds on the east side of the garden, what is the probability that all of them are dill seeds? $\newline$ Write your answer as a decimal rounded to four decimal places. $\newline$ ____

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Find probabilities using combinations and permutations

Full solution

Q. Erin bought

9

seeds in order to plant an herb garden for her grandma. Of the seeds she bought,

7

were dill seeds.

\newline

If Erin chooses to plant

6

random seeds on the east side of the garden, what is the probability that all of them are dill seeds?

\newline

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

\newline

____

Calculate total ways: Calculate the total number of ways to choose $6$ seeds from $9$ . $\newline$ \text{\textsubscript{9}}C\text{\textsubscript{6}} = \frac{9!}{6!(9-6)!} $\newline$ = $\frac{9!}{6!3!}$ $\newline$ = $\frac{9 \times 8 \times 7 \times 6!}{6! \times 3 \times 2 \times 1}$ $\newline$ = $84$
Calculate dill seeds ways: Calculate the number of ways to choose $6$ dill seeds from $7$ . $<sub>7</sub>C<sub>6</sub> = \frac{7!}{6!(7-6)!} = \frac{7!}{6!1!} = \frac{7 \times 6!}{6! \times 1} = 7$
Find probability: Find the probability that all chosen seeds are dill seeds. $\newline$ Probability = Favorable outcomes / Total possible outcomes $\newline$ = $\frac{7}{84}$ $\newline$ = $\frac{1}{12}$

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