Question

how all your work.

1. suppose ed is going to build a playlist that contains 9 songs. in how many different ways can ed arrange the 9 songs on the playlist?
2. suppose 7 cars start at a car race. in how many ways can the top 3 cars finish the race?
3. how many different simple random samples of size 4 can be obtained from a population whose size is 50?

Explanation:

Step1: Solve the first problem (arranging 9 songs)

This is a permutation of \(n = 9\) objects taken \(n=9\) at a time. The formula for permutations \(P(n,r)=\frac{n!}{(n - r)!}\), when \(n=r\), \(P(n,n)=n!\). So, \(9! = 9\times8\times7\times6\times5\times4\times3\times2\times1\)

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Step2: Solve the second problem (top 3 cars out of 7)

Here \(n = 7\) and \(r=3\). Using the permutation formula \(P(n,r)=\frac{n!}{(n - r)!}\), we have \(P(7,3)=\frac{7!}{(7 - 3)!}=\frac{7!}{4!}\)

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Step3: Solve the third problem (simple - random samples of size 4 from a population of 50)

This is a combination problem. The formula for combinations \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 50\) and \(r = 4\)

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Answer:

1. \(362880\)
2. \(210\)
3. \(230300\)