Question

question 9
4 pts
according to the website of the lt. governor of the state of hawaii, the state has the highest rate of homelessness per capita in the nation. unfortunately, the state is also sometimes a target by the homeless from other states who try to get to hawaii for its perennial nice weather. such people are identified and face either being arrested or given a free one - way ticket back to wherever they came from.
at one homeless shelter in hawaii, there are 12 individuals from new york and 16 from louisiana. of these individuals, what is the probability that 7 individuals from new york and 10 from louisiana accept to be given a free one - way ticket back to where they came from in order to avoid being arrested?
note: if your answer has up to four decimal places, please enter it in the box below without rounding the number. however, if your answer has more than four decimal places, please round your answer to four decimal places.

Explanation:

Step1: Calculate total number of individuals

Total individuals \(n = 12+16=28\). Number of individuals to be selected \(k=7 + 10=17\)

Step2: Use combination formula

The number of ways to choose \(7\) from \(12\) (New - Yorkers) is \(C(12,7)=\frac{12!}{7!(12 - 7)!}=\frac{12!}{7!5!}=\frac{12\times11\times10\times9\times8}{5\times4\times3\times2\times1}=792\)
The number of ways to choose \(10\) from \(16\) (Louisianans) is \(C(16,10)=\frac{16!}{10!(16 - 10)!}=\frac{16!}{10!6!}=\frac{16\times15\times14\times13\times12\times11}{6\times5\times4\times3\times2\times1}=8008\)
The number of ways to choose \(17\) from \(28\) is \(C(28,17)=\frac{28!}{17!(28 - 17)!}=\frac{28!}{17!11!}\)

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Step3: Calculate probability

The probability \(P=\frac{C(12,7)\times C(16,10)}{C(28,17)}\)

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Answer:

\(0.0020\)