Question

Using the integers 2,3,4,5,
How many 3-digit odd numbers less than 300 can be formed if no repetition of digits is allowed?
Please explain and show work.

Answer 1

Since it's an odd number LESS than 300 we know that the first number can only be 2 and therefore we have only 1 choice for the first unit. Since it's an ODD number we know that the last unit is either 3 or 5 (2 choices). No we are left with either 4 and 3 or 5 (depending on which one was chosen for the last unit), therefore we have 2 choices for the middle unit. Hence, the answer is 1x2x2 = 4 numbers.
Just for assurance, let's list out the numbers
235
245
253
243