Question

Probability Question

Answer 1

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

Answer 2

whats your first step?

Answer 3

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 \(\large \dfrac{1}{^5C_3}\)

Answer 4

method2 :
consider a string of length \(3\) :


how many total strings of length 3 can you make by using the letters \(\{A,B,C,D,E\}\) ?

Answer 5

\(\large 3^{3}\) ?

Answer 6

Nope, how many choices are there for the first letter ?

Answer 7

5

Answer 8

5*4*3=60

Answer 9

Yes, thats the total number of strings.

How many of those strings have A,B,C in any order ?

Answer 10

6

Answer 11

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

Answer 12

6 is right

Answer 13

total number of strings = 60
number of strings in favor = 6

divide to get the probability

Answer 14

thnx!