Question

How many positive odd integers less than 500 can be formed from the digits 3, 4, and 5 without repetition?

Answer 1

only the 2 or 3 can be used at the front
without the odd restriction:

number of such number = 2x2x1 = 4

we can actually list them:
345, 354, 435, 453

notice that 1 of them is even

so there are only 3 of them

or

suppose it starts with the 4:
only the two odds are left, so number of such numbers = 1x2x1 = 2
suppose it starts with a 3, so only one odd is left to use in the unit place, leaving the remaining one for the tens place
number of ways = 1x1x1 = 1
total of 3