PROBLEM SOLVING. Probability and Combination

1. If an editor must arrange five articles in a magazine and there are eight articles available, how many different arrangements are possible?
2. In how many different ways can the letters of the word CORPORATION be arranged so that the vowels always come together?
3. From 3 red, 4 green, and 5 yellow plastic balls, how many selections consisting of 6 balls are possible if 2 of each are to be selected?
4. How many odd three-digit 2 points numbers can be formed from the digits 1,2,3,4,5 if each digits can only be used once?
5. In how many ways can 4 boys and 3 girls sit in a row if the boys and girls must alternate?