Question

Belle bought 18 seeds in order to plant an herb garden for her grandma. Of the seeds she bought, 10 were parsley seeds.

If Belle chooses to plant 15 random seeds on the east side of the garden, what is the probability that exactly 9 of the chosen seeds are parsley seeds?

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

Answer 1

0.3431

Explanation:

Here, it can work well to consider the seeds from the group of 18 that are NOT selected to be part of the group of 15 that are planted.

There are 18C3 = 816 ways to choose 3 seeds from 18 NOT to plant.

We are interested in the number of ways exactly one of the 10 parsley seeds can be chosen NOT to plant. For each of the 10C1 = 10 ways we can ignore exactly 1 parsley seed, there are also 8C2 = 28 ways to ignore two non-parsley seeds from the 8 that are non-parsley seeds.

That is, there are 10×28 = 280 ways to choose to ignore 1 parsley seed and 2 non-parsley seeds.

So, the probability of interest is 280/816 ≈ 0.3431.

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The notation nCk is used to represent the expression n!/(k!(n-k)!), the number of ways k objects can be chosen from a group of n. It can be pronounced "n choose k".