Review problem. I have the answers. Don't know how to get them. Answers in brackets.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the main frame. Suppose a paricular city has 25 of these buses, and cracks have actually appeared on 8 of them.

a.)How many ways are there to select a sample of 5 buses from the 25 for a thorough inspection? [53130]

b.) In how many ways can a sample of 5 buses contain exactly 4 with visible cracks? [1190]

c.) If a sample of 5 buses is chosen at random, what is the probability that exactly 4 of the 5 will have visible cracks? [.0224]

d.) If buses are selected as in part (c), what is the probability that at least 4 of those selected will have visible cracks? [.0235]

2. Relevant equations

[tex]Permutations = P_{k,n} = \frac{n!}{(n-k)!}[/tex]

[tex]Combinations = \begin{pmatrix}

n\\

k

\end{pmatrix}= \frac{n!}{k!(n-k)!}[/tex]

3. The attempt at a solution

a.) I'm looking for the total number of combinations of choosing 5 buses out of the 25 buses. Therefore

[tex]Combinations = \begin{pmatrix}

n\\

k

\end{pmatrix} = \frac{n!}{k!(n-k)!} = \frac{25!}{5!(25-5)!} = 53130[/tex]

b.) I don't know how to set it up.

c.) Didn't attempt it because I can't do (b).

d.) Didn't attempt it because I can't do (b).

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# Homework Help: Permutations and Combinations of samples

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