Did I do this problem right?
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?
Answer: 3*10*9=270.
correct
To determine if you did the problem right, we can go through the steps together.
First, let's break down the problem. We are looking for three-symbol codes in the format letter-number-number. The letters we can use are S, P, and Y. We also have to choose two digits from the set {0, 1, 2, ..., 9} without repetition.
Now let's calculate the number of possible combinations step by step:
1. For the first symbol (which is a letter), we have three choices: S, P, or Y.
2. For the second symbol (which is a number), we have ten choices since we can select any digit from 0 to 9.
3. Finally, for the third symbol (another number), we have nine choices left since we can't repeat the digit we used for the second symbol.
To find the total number of combinations, we multiply the choices for each symbol together:
3 (choices for the first symbol) * 10 (choices for the second symbol) * 9 (choices for the third symbol) = 270.
So, the answer is indeed 270. Congratulations, you did the problem correctly!