SOLUTION: How many four-digit odd numbers less than 6000 can be formed using the digits 2,4,6,7,8,9?

2,4,6,7,8,9

We choose the fourth digit first:  There are 2 ways to select the fourth
digit, either 7 or 9, so that the number will be odd.

Next we choose the first digit: There are 2 ways to select the fourth
digit, either 2 or 4, so that the number will be less than 6000.

Next we choose the second digit: There are 4 ways to select the second
digit, any of the four remaining digits.


Finally we choose the third digit: There are 3 ways to select the second
digit as any of the three remaining digits.

So the number of such four-digit numbers is 2*2*4*3=48

Here they all are:

2467  2469  2479  2487  2489  2497
2647  2649  2679  2687  2689  2697
2749  2769  2789  2847  2849  2867
2869  2879  2897  2947  2967  2987
4267  4269  4279  4287  4289  4297
4627  4629  4679  4687  4689  4697
4729  4769  4789  4827  4829  4867
4869  4879  4897  4927  4967  4987

Edwin