## mathmath333 one year ago Probability Question

1. 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}}

2. anonymous

3. 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 $$\large \dfrac{1}{^5C_3}$$

4. 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 $$\{A,B,C,D,E\}$$ ?

5. mathmath333

$$\large 3^{3}$$ ?

6. ganeshie8

Nope, how many choices are there for the first letter ? |dw:1439647853502:dw|

7. mathmath333

5

8. mathmath333

5*4*3=60

9. ganeshie8

Yes, thats the total number of strings. How many of those strings have A,B,C in any order ?

10. mathmath333

6

11. ganeshie8

In other words, how many 3 bit strings can you make using just the letters A,B,C

12. ganeshie8

6 is right

13. ganeshie8

total number of strings = 60 number of strings in favor = 6 divide to get the probability

14. mathmath333

thnx!