This is permutations with repetition. The answer is 4^4 = 256 total permutations. Since 2 of the digits used are odd (and 2 are even), then half of the possibilities will be odd: 128 odd numbers.
500
It is 120 if the digits cannot be repeated.
4*3*2*1 = 24
6*5*4*3*2*1=720
That would be 4! = 4 * 3 * 2 * 1 = 24
24
500
5040 different 4 digit numbers can be formed with the digits 123456789. This is assuming that no digits are repeated with each combination.
There are 5*4*3 = 60 such numbers.
1 set
It is 120 if the digits cannot be repeated.
This permutation problem depends on whether the numbers are allowed to be repeated. If they are, there are a possible 9999 numbers, starting with 0001 and running sequentially to 9999. If they are not allowed to be repeated, there are a possible 5040 combinations.
27 if the digits can be repeated. 6 if not.
3x3x3=27
36
6*6*3 = 108 numbers.
4*3*2*1 = 24