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e-lub [12.9K]
3 years ago
10

There were 23 students running in a race. How many different arrangements of first, second, and third place are possible?

Mathematics
1 answer:
Alex787 [66]3 years ago
7 0

Answer:

10626 different arrangements

Step-by-step explanation:

As we have a total of 23 students and we want to form groups of 3, where the order of the 3 students matters, we can solve this problem using a permutation of 23 choose 3.

The formula for a permutation of n choose p is:

P(n,p) = n! / (n-p)!

So, using n = 23 and p = 3, we have:

P(23,3) = 23! / (23-3)! = 23! / 20! = 23 * 22 * 21 = 10626

So we have a total of 10626 different arrangements of first, second and third place.

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The p value for this case would be given by:

p_v =2*P(z  

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Step-by-step explanation:

Information given

\bar X=31.1 represent the sample mean  

\sigma=1.3 represent the population standard deviation

n=140 sample size  

\mu_o =31.3 represent the value that we want to test  

\alpha=0.02 represent the significance level for the hypothesis test.  

z would represent the statistic

p_v represent the p value

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We want to test if the true mean is equal to 31.3 MPG, the system of hypothesis would be:  

Null hypothesis:\mu =31.3  

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Since we know the population deviation, the statistic is given by

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)  

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