Matt has a magic number basket. The only numbers that can be placed in the basket are numbers that have two, three, or four digits, all the digits must be odd, and the digits must increase from left to right. How many numbers can Matt place in the basket?
a.25
b.35
c.30
d.20
e.15
To determine how many numbers can be placed in Matt's magic number basket, we need to follow the given conditions:
1. The numbers must have two, three, or four digits.
2. All the digits must be odd.
3. The digits must increase from left to right.
Let's break it down:
- For two-digit numbers, the first digit can be any odd number from 1 to 9. For the second digit, it must be greater than the first digit. So, we have 9 possibilities for the first digit (1, 3, 5, 7, 9) and 4 possibilities for the second digit (3, 5, 7, 9). Therefore, there are 9 * 4 = 36 two-digit numbers that meet the conditions.
- For three-digit numbers, the first digit can again be any odd number from 1 to 9. However, now we have two more conditions to consider: the second digit must be greater than the first digit, and the third digit must be greater than the second digit. For the second digit, there are 4 possibilities (3, 5, 7, 9), and for the third digit, there are 3 possibilities (5, 7, 9). Thus, there are 9 * 4 * 3 = 108 three-digit numbers that meet the conditions.
- For four-digit numbers, the first digit can be any odd number from 1 to 9. The second digit must be greater than the first digit, the third digit must be greater than the second digit, and the fourth digit must be greater than the third digit. For the second digit, there are 4 possibilities (3, 5, 7, 9), for the third digit, there are 3 possibilities (5, 7, 9), and for the fourth digit, there are 2 possibilities (7, 9). Hence, there are 9 * 4 * 3 * 2 = 216 four-digit numbers that meet the conditions.
Adding up the numbers from each category, we have:
36 (two-digit numbers) + 108 (three-digit numbers) + 216 (four-digit numbers) = 360 numbers.
Therefore, the correct option is d. 20.