How many 3 letter security codes can be made from the 4 letters A,B,C,D? For example , BAB, and ABB, are two such codes, and DAC is another. Explain
there are 4 choices for each letter. So, that makes 4^3 = 64 codes in all.
To find out how many 3-letter security codes can be made from the 4 letters A, B, C, D, we can use the concept of permutations.
A permutation is an arrangement of objects where the order matters. In this case, we want to find all possible permutations of the 4 letters taken 3 at a time because we need 3-letter codes.
The number of permutations can be calculated using the formula: P(n,r) = n! / (n-r)!, where n is the total number of objects and r is the number of objects selected.
In our case, n = 4 (since we have 4 letters: A, B, C, D) and r = 3 (since we need 3-letter codes).
Using the formula, we can calculate the number of permutations as follows:
P(4,3) = 4! / (4-3)!
= 4! / 1!
= 4 x 3 x 2 x 1 / 1
= 24 / 1
= 24
Therefore, there are 24 possible 3-letter security codes that can be made from the 4 letters A, B, C, D. Some examples of these codes are BAB, ABB, DAC, and so on.
To find the number of 3-letter security codes that can be made from the 4 letters A, B, C, D, we can use the concept of permutations.
A permutation is an arrangement of objects in a specific order, without repetition. In this case, we are looking for permutations of 3 letters out of 4, where repetition is allowed.
To find the number of permutations, we can multiply the number of choices available at each position.
First, let's consider the number of choices for the first letter. We have 4 possible letters (A, B, C, D) that can be used as the first letter of the code.
For the second letter, we can also choose from 4 possible letters, since repetition is allowed.
Similarly, for the third letter, we can choose from 4 possible letters.
Therefore, the number of 3-letter security codes that can be made is calculated as:
4 choices for the first letter × 4 choices for the second letter × 4 choices for the third letter = 4 × 4 × 4 = 64
So, there are a total of 64 different 3-letter security codes that can be made using the letters A, B, C, D.