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Bas_tet [7]
3 years ago
5

In a set of 25 aluminum castings, four castings are defective (D), and the remaining twenty-one are good (G). A quality control

inspector randomly selects three of the twenty-five castings without replacement to test. The sample space for selecting the group to test contains ____________ elementary events.
Mathematics
1 answer:
lianna [129]3 years ago
6 0

Answer:

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

Step-by-step explanation:

There are a total of <em>N</em> = 25 aluminum castings.

Of these 25 aluminum castings, <em>n</em>₁ = 4 castings are defective (D) and <em>n</em>₂ = 21 are good (G).

It is provided that a quality control inspector randomly selects three of the twenty-five castings without replacement to test.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

{n\choose k}=\frac{n!}{k!(n-k)!}

Compute the number of samples that are possible as follows:

{25\choose 3}=\frac{25!}{3!\times (25-3)!}

      =\frac{25\times 24\times 23\times 22!}{3!\times 22!}\\\\=\frac{25\times 24\times 23}{3\times 2\times 1}\\\\=2300

The sample space for selecting the group to test contains <u>2,300</u> elementary events.

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