Question

The seven cards are [A A A B B R R] how do I solve this?

Answer 1

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:

`\begin{gathered} C(n,k)=(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)=(7!)/((7-4)!4!)=(5040)/(6*24)=(5040)/(144)=35 \end{gathered}`

There are 35 possible arrangements for these 4 cards.