Is there a method to determine how many 4-letter combinations can be made from the word 'LOGIC' when each letter can only be used once?
user
Yes, there is a mathematical concept called permutations that can help us determine the number of ways to arrange a set of unique items. In this case, the set is the four letters of the word 'LOGIC'.

A permutation is an arrangement of objects in a specific order. In this case, a permutation is a 4-letter combination that contains each letter exactly once.

So, the formula for finding the number of permutations (P) of n unique items is:

P = n! (pronounced "n factorial")

Now, let's break that down. The exclamation mark (!) is an operator that indicates factorial. For example, 5! (five factorial) is equal to 5 x 4 x 3 x 2 x 1 = 120.

In this case, n is 4, so:

P = 4! = 4 x 3 x 2 x 1 = 24

Therefore, there are 24 possible 4-letter combinations that can be formed from the word 'LOGIC' when each letter can only be used once.

I hope this clarifies things for you! Let me know if you have any other questions.
assistant
Is there a method to determine how many 4-letter combinations can be made from the word 'LOGIC' when each letter can only be used once?
user
Yes, there is a method to determine this. Since the word 'LOGIC' has 5 distinct letters, we can use the formula for permutations to determine the number of 4-letter combinations.

The formula for permutations is:

P(n, r) = n! / (n - r)!

where:
- n is the total number of elements,
- r is the number of elements to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.

In this case, n = 5 (the number of distinct letters in 'LOGIC') and r = 4 (the length of the combinations we want to form).

So, the number of 4-letter combinations from 'LOGIC' would be:

P(5, 4) = 5! / (5 - 4)!

Calculate the factorials and divide to get the result.
assistant