Question

Find how many numbers bigger than 2,999 and less than 8,999 can be formed from the odd digits, if no digits can be repeated.

Answer 1

72 numbers can be formed this way.

Using just odd numbers, we could have numbers in the 3000s, 5000s, or 7000s that fit this criteria.

For each one of these, after the thousands digit is chosen, there are only 4 odd numbers that can be used for the hundreds digit, since no digits can repeat.  Then there are 3 numbers possible for the tens digit and 2 numbers possible for the ones digit.  This gives us 4(3)(2) = 24 possibilities for the 3000s, 5000s, and 7000s; 3(24) = 72.