How many three-symbol codes (letter-number-number) can be made from the letters S, P, Y and two digits from the set {0, 1, 2, …,9} without repetition?

I think I am suppose to match each letter with a number until I exhaust all possibilities but I am not sure can you help please?

for the letter: determine first how many letters are possible,,

there are 3 *S, P, Y
for the first number: how many are possible,,
there are 10 *0,1,2,..9
for the second number: since no repetition is allowed, there only 9 possible,,,
then multiply:
3*10*9 = 270 possibilities

so there,, =)

Wonderful, Thanks for your hel:)

Certainly! To find the number of three-symbol codes that can be made according to the given conditions, you need to follow a step-by-step approach.

Step 1: Determine the number of choices for the letter symbols.
In this case, you have three letters: S, P, and Y. Since repetition is not allowed, you can select one letter at a time from the given set without replacement. Hence, you have three choices for the first letter, two choices for the second letter, and one choice for the third letter.

Step 2: Determine the number of choices for the number symbols.
You need two digits from the set {0, 1, 2, …, 9} without repetition. Since repetition is not allowed, you can also select one digit at a time without replacement. Hence, you have ten choices for the first digit and nine choices for the second digit.

Step 3: Combine the choices.
To calculate the total number of three-symbol codes, multiply the number of choices for each step:

Total number of codes = (number of choices for letters) * (number of choices for first digit) * (number of choices for second digit)
= 3 * 2 * 1 * 10 * 9

Therefore, the total number of three-symbol codes that can be made is 3 * 2 * 1 * 10 * 9 = 540.

So, there are 540 different three-symbol codes (letter-number-number) that can be made from the letters S, P, Y, and two digits from the set {0, 1, 2, …, 9} without repetition.