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Jason is running tests on the impact strength of 9 types of steel plating. These tests...

Jason is running tests on the impact strength of 9 types of steel plating. These tests will be conducted in random order. If four of these platings come from the same manufacturer, what is the probability that the tests on these platings will be run back to back to back to back?

Math   Statistics-And-Probability   
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Answer #1

Since the order of the platings tested is important, we can arrange the 9 tests in 9! Ways.

Therefore, no. of elements in the sample space = n(S) = 9!

Now, let A denote the event that the 4 platings coming from the same manufacturer are tested back to back.

We have to find P(A).

Now, consider the 4 platings as a single unit. (i.e. counts these 4 platings as 1). This bunch of 4 platings combined into 1 can be arranged in any order with the remaining 5 platings. This means that we have to arrange 6 platings (wherever we place the combined unit it will imply that the 4 platings are placed together). So the 6 platings can be arranged in 6! ways. Also, the 4 platings by the same manufacturer can be arranged within themselves in 4! ways.

n(A) = 6! × 4! = 17280

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