Please solve for me.

Permutations Assignment 1. How many ways can you arrange the letters in the word REDCOATS, 1. with no restrictions 2. if the word must start with a vowel? 3. if it must start with a consonant? 4. if the 2nd, 5", and 7' letters must be vowels? 5. if it must start with a vowel and end with a consonant 6. if the smaller word RED must appear in the arrangement 7. if the vowels must not be together 2. How many 8 letter words can be made from the word ABSOLUTE 1. with no restrictions 2. if it must start with an A Shewore 3. if A and B must be together 4. if it A and B must be together at the front of the word 5. if B must always follow A 6. if ABS must be together 3. In the first annual Run for the Factorial Road Race, 1. if there are only 10 racers how many different finishes can there be? 2. if there are only 10 racers, how many ways can 1st, 2nd, and 3rd be determined? 3. if in the second year they are up to 20 Racers, how many ways can 1st, 2nd, and 3rd be determined? 4. if in it's third year there are 30 racers and the top 20 advance to the Permutation Parade. How many different top twenty finished are there? 4. How many ways can 5 people be seated on a bench? WOH SP 5. How many ways can 3 girls and three boys sit in a row if boys and girls must alternate? 6. How many arrangements are there of: 1. 30 students in a classroom with 30 desks 2. 17 students in a classroom with 25 desks 3. 4 ski tows up the hill and 7 routes down the hill 4 . A room if the interior decorator has selected 18 Carpet Swatches, 25 Wall Patterns and T Paint hues