4. How many odd positive integers less than 500 can be written using

the numbers 3, 4, 5, 6, and 7?

Answer:

48

Step-by-step explanation:

There are 3 one-digit numbers: 3, 5, 7.

There are 15 two-digit numbers: 33, 35, 37, 43, 45, 47, 53, 55, 57, 63, 65, 67, 73, 75, 77.

There are 30 3-digit numbers, from 333 to 477. The leading digit must be 3 or 4; the trailing digit must be 3, 5, or 7; and the middle digit can be any of the 5 digits, for a total of 2*5*3 = 30 possible 3-digit numbers. (That is, 300 or 400 can be added to any of the 15 2-digit numbers.)

Using the given digits, 3+15+30 = 48 odd numbers less than 500 can be written.