Problem

Outside a home, there is a 4-key keypad with letters A, B, C, and D that can be used to open the garage if the correct four-letter code is entered. Each key may be used only once. How many codes are possible?
The number of possible codes is

Answer

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Answer

Final Answer: The number of possible codes is \(\boxed{24}\).

Steps

Step 1 :We are given a 4-key keypad with letters A, B, C, and D. We need to find out how many different 4-letter codes we can make with these letters, where each letter can only be used once.

Step 2 :This is a permutation problem. The formula for permutations is \(nPr = \frac{n!}{(n-r)!}\), where n is the number of items to choose from, r is how many we choose, and '!' denotes factorial.

Step 3 :In this case, n = r = 4, so the formula simplifies to \(4! = 4 \times 3 \times 2 \times 1\).

Step 4 :Calculating the above expression, we get \(4! = 24\).

Step 5 :Final Answer: The number of possible codes is \(\boxed{24}\).

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