How many three-symbol codes (letter, letter, number) can be made from the letters S, P, Y and one digit fro the set {0, 1, 2,...9} without repitition?
What and how do I get started?
What is 3*2*10 ?
60
To find the number of three-symbol codes that can be made from the letters S, P, Y, and one digit from the set {0, 1, 2,...9} without repetition, you can use basic principles of counting. Here's how you can get started:
Step 1: Determine the number of choices for each position:
- For the first position, you can choose from three letters: S, P, or Y.
- For the second position, you can choose from the remaining two letters after using one letter in the first position.
- For the third position, you can choose from the 10 digits from the set {0, 1, 2,...9}.
Step 2: Multiply the number of choices for each position:
Since each position is independent of the others, you can multiply the number of choices for each position together to find the total number of codes. Therefore, the total number of three-symbol codes can be calculated as follows:
Number of codes = Number of choices for the first position * Number of choices for the second position * Number of choices for the third position
Number of codes = 3 * 2 * 10
Step 3: Calculate the total number of codes:
Multiply the numbers together to get the final answer:
Number of codes = 3 * 2 * 10 = 60
So, there are a total of 60 three-symbol codes that can be made from the letters S, P, Y, and one digit from the set {0, 1, 2,...9} without repetition.