how many three letter symbols can be formed from the letters A,C,K,L, & M without repetition?

so far I have 12

To find the number of three-letter symbols that can be formed from the letters A, C, K, L, and M without repetition, you can use the concept of permutations.

Permutations are arrangements of objects without repetition, where the order of the objects matters. In this case, we want to find the number of three-letter symbols, so we need to calculate the number of permutations of three objects taken from a set of five.

The formula to calculate permutations is given by:

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

Where:
- n is the total number of objects in the set (5 in this case)
- r is the number of objects taken at a time (3 in this case)
- "!" denotes factorial, which means multiplying a number by all positive integers less than it down to 1

Using the formula, we can calculate the number of three-letter symbols:

P(5, 3) = 5! / (5 - 3)!
= 5! / 2!
= (5 x 4 x 3 x 2 x 1) / (2 x 1)
= (120) / (2)
= 60

Therefore, there are 60 different three-letter symbols that can be formed from the letters A, C, K, L, and M without repetition.