The given information is:
- The seven cards are A,A,A,A,B,B,R,R
Now, the 7 cards are shuffled, and 4 of the 7 cards are chosen at random and arranged in a random order in a straight line.
To find the total number of arrangements of these 4 cards, let's analyze the possibilities:
[tex]\begin{gathered} C(n,k)=\frac{n!}{(n-k)!k!} \\ \\ This\text{ is a combination since the order doesn't matter} \\ n\text{ is the total number of letters 7, and k is the number of letters we chose 4} \\ So: \\ C(7,4)=\frac{7!}{(7-4)!4!}=\frac{5040}{6*24}=\frac{5040}{144}=35 \end{gathered}[/tex]
There are 35 possible arrangements for these 4 cards.
