Here Is an Incorrect Solution to a Problem $\left. \begin{array} { l } 4 \\ 2 \end{array} \right)$

question 152

Essay

Here is an incorrect solution to a problem. Find the error, explain why it is not correct, and give the correct answer. "Problem: Find the number of ways to get two pairs of two different ranks (such as 2 jacks and 2 fives) in a 4-card hand from an ordinary deck of 52 cards."
"Solution: There are 13 ways to get a rank (such as "kings") for the first pair and ( $\left. \begin{array} { l } 4 \\ 2 \end{array} \right)$ ways to get a pair of that rank. Similarly, there are 12 ways to get a rank (such as "sevens") for the second pair and $\left( \begin{array} { l } 4 \\ 2 \end{array} \right)$ ways to get a pair of that rank. Therefore there are $13 \cdot \left( \begin{array} { l } 4 \\ 2 \end{array} \right) \cdot 12 \cdot \left( \begin{array} { l } 4 \\ 2 \end{array} \right)$ ways to get 2 pairs."

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Definitions:

Non-servo Drum Brake

A type of drum brake system that relies on a simpler mechanism without servo action, often found in older or less complex vehicles.

Leading Shoe

A component of drum brake systems, it refers to the brake shoe positioned towards the front of the vehicle that comes into contact with the brake drum first when brakes are applied.

Energized

Describes an electrical component that is carrying current or a system that is under power.

Disc/drum Hydraulic Brake

A type of brake system that uses hydraulic fluid to press brake pads against a disc or shoes against a drum to slow or stop a vehicle.