Lark has forgotten her locker combination. It is a sequence of three numbers, each in the range from 1 to 30, inclusive. She knows that the first number is odd, the second number is even, and the third number is a multiple of 3. How many combinations could possibly be Lark's?
There are 15 odd numbers, 15 even numbers, and 10 multiples of 3, making for $15^2\cdot 10 = 225 \cdot 10 = \boxed{2250}$ combinations total.
2250
Level 2
Counting & Probability
Problem: Lark has forgotten her locker combination. It is a sequence of three numbers, each in the range from 1 to 30, inclusive. She knows that the first number is odd, the second number is even, and the third number is a multiple of 3. How many combinations could possibly be Lark's?
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To determine the total number of combinations for Lark's locker, we need to analyze the constraints for each of the three numbers in the combination.

1. The first number must be odd. The odd numbers between 1 and 30 are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29. This gives us a total of 15 possible choices for the first number.

2. The second number must be even. The even numbers between 1 and 30 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30. This results in 15 possible choices for the second number.

3. The third number must be a multiple of 3. The multiples of 3 between 1 and 30 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. This gives us 10 possible choices for the third number.

To find the total number of combinations, we multiply the number of choices for each position in the combination:

Total combinations = (Number of choices for the first number) × (Number of choices for the second number) × (Number of choices for the third number)

Calculating this gives:

Total combinations = 15 (odd numbers) × 15 (even numbers) × 10 (multiples of 3) = 2250.

Thus, the final answer is 2250.<|END_OF_LATENT|> The final answer is $2250$.