mathmath333
  • mathmath333
Probability Question
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align}& \normalsize \text{In a relay race there are five teams A, B, C, D and E.}\hspace{.33em}\\~\\ & \normalsize \text{(a) What is the probability that A, B and C}\hspace{.33em}\\~\\ & \normalsize \text{are first three to finish (in any order)}\hspace{.33em}\\~\\ & \normalsize \text{(Assume that all finishing orders are equally likely)}\hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
whats your first step?
ganeshie8
  • ganeshie8
lets 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 \(\large \dfrac{1}{^5C_3}\)

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ganeshie8
  • ganeshie8
method2 : 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
  • mathmath333
\(\large 3^{3}\) ?
ganeshie8
  • ganeshie8
Nope, how many choices are there for the first letter ? |dw:1439647853502:dw|
mathmath333
  • mathmath333
5
mathmath333
  • mathmath333
5*4*3=60
ganeshie8
  • ganeshie8
Yes, thats the total number of strings. How many of those strings have A,B,C in any order ?
mathmath333
  • mathmath333
6
ganeshie8
  • ganeshie8
In other words, how many 3 bit strings can you make using just the letters A,B,C
ganeshie8
  • ganeshie8
6 is right
ganeshie8
  • ganeshie8
total number of strings = 60 number of strings in favor = 6 divide to get the probability
mathmath333
  • mathmath333
thnx!

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