Please help-I'm really mixed up

How do I find the permutations of the first 12 letters taken 3 at a time?

I have a ton of these to do and really don't understand them at all-

permutations:

That means all the arrangements of three made from the 12 when order is important. For example
ABC and ACB and BAC and BCA and CAB and CBA are all different.
The formula for that is
n!/[n-r]!
here n = 12 and r = 3
so we have
12!/9! which is 12*11*10 = 132
That is what you asked.

To answer what is coming next, combinations of n taken r at a time where order is NOT important are called indeed combinations and the formula is logically enough the permutation formula divided by r!
C(n,r) = n!/[ r! (n-r)! ]

Thank you for the explanation-it actually makes sense now

I'm here to help! Finding permutations can be challenging at first, but it becomes easier with practice. To find the permutations of the first 12 letters taken 3 at a time, you can follow these steps:

Step 1: Understand the concept
Before we start, it's important to understand what permutations are. Permutations are the different ways in which a set of elements can be arranged. In this case, we want to find all the possible arrangements of the first 12 letters taken 3 at a time.

Step 2: Calculate the number of permutations
To find the number of permutations, we can use the formula for permutations without repetition:

P(n, r) = n! / (n - r)!
Where P(n, r) represents the number of permutations of n items taken r at a time, and "!" denotes factorial.

In our case, n = 12 (the total number of items) and r = 3 (the number of items taken at a time). Therefore, the number of permutations can be calculated as follows:

P(12, 3) = 12! / (12 - 3)! = 12! / 9!

Step 3: Evaluate the factorial
To calculate the factorials, we need to understand what they represent. The factorial of a number is the product of all positive integers from 1 to that number.

For example, 5! (read as "5 factorial") is calculated as follows:
5! = 5 x 4 x 3 x 2 x 1 = 120

You can use a calculator or a math software to calculate the factorial of a larger number like 12. Once you have the factorial values for both 12 and 9, substitute them into the formula:

P(12, 3) = 12! / 9!

This will give you the total number of permutations of the first 12 letters taken 3 at a time.

Step 4: Calculate the actual permutations
To calculate the actual permutations, you can use various methods depending on your preference and the tools available to you. One approach is to use a permutation calculator or software, which can generate all the possible arrangements for you.

Alternatively, you can list out all the possible arrangements manually by systematically rearranging the letters. Start by selecting one letter, then choose another from the remaining letters, and finally select the third letter. Repeat this process for all possible combinations.

Remember that the order matters in permutations, so ABC is different from ACB or BAC, etc.

By following these steps, you should be able to find the permutations of the first 12 letters taken 3 at a time. If you have any specific questions or need further assistance, feel free to ask!