How many three-letter code symbols can be formed from the letters A, C, K, L , and M without repetition?
Noting that ACK is not the same as KAC,
You can choose from 5 letters for your first
Then you can choose from 4 letters for your second.
Finally you can choose from 3 letters for your first
So you can choose in 5 * 4 * 3 ways.
To calculate the number of three-letter code symbols that can be formed without repetition from the letters A, C, K, L, and M, we can use the concept of permutations.
The number of permutations of n items taken r at a time is given by the formula:
P(n, r) = n! / (n - r)!
Where '!' denotes factorial.
In this case, we have 5 letters to choose from, and we need to choose 3 without repetition.
Therefore, the number of three-letter code symbols that can be formed is:
P(5, 3) = 5! / (5 - 3)! = 5! / 2! = (5 × 4 × 3 × 2 × 1) / (2 × 1) = 5 × 4 × 3 = 60
So, there are 60 possible three-letter code symbols that can be formed from the letters A, C, K, L, and M without repetition.
To find the number of three-letter code symbols that can be formed from the given letters without repetition, we can use the concept of permutations.
Permutations are arrangements of objects where the order matters and repetition is not allowed. The formula to calculate permutations is:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects to be selected.
In this case, we have 5 letters (A, C, K, L, and M) and we need to select 3 letters to form a symbol.
Using the permutation formula:
P(5, 3) = 5! / (5 - 3)!
= 5! / 2!
= (5 * 4 * 3 * 2 * 1) / (2 * 1)
= 60 / 2
= 30
Therefore, there are 30 different three-letter code symbols that can be formed from the given letters without repetition.