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mathmath333
 one year ago
Probability Question
mathmath333
 one year ago
Probability Question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align}& \normalsize \text{In a relay race there are five teams A, B, C, D and E.}\hspace{.33em}\\~\\ & \normalsize \text{(a) What is the probability that A, B and C}\hspace{.33em}\\~\\ & \normalsize \text{are first three to finish (in any order)}\hspace{.33em}\\~\\ & \normalsize \text{(Assume that all finishing orders are equally likely)}\hspace{.33em}\\~\\ \end{align}}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0whats your first step?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1lets do this problem in two ways : method 1 we can choose any \(3\) people from \(5\) people in \(\large ^5C_3\) ways, but only the selection \(\{A,B,C\}\) is our favorite, so the probability is \(\large \dfrac{1}{^5C_3}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1method2 : consider a string of length \(3\) : dw:1439647639858:dw how many total strings of length 3 can you make by using the letters \(\{A,B,C,D,E\}\) ?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large 3^{3}\) ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Nope, how many choices are there for the first letter ? dw:1439647853502:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Yes, thats the total number of strings. How many of those strings have A,B,C in any order ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1In other words, how many 3 bit strings can you make using just the letters A,B,C

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1total number of strings = 60 number of strings in favor = 6 divide to get the probability
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