these have to do with permutations please answer all of the questions and show your work.

1)How many combinations can be formed from the letters of the word HEXAGON taking three at a time?

2)How many positive 4-digit integers can be made if 2 different digits are selected from {1, 2, 3, 4} and 2 different digits are selected from {5, 6,7, 8, 9}?

3)A small class consists of 5 boys and 7 girls. How many groups can be selected from this class that consist of3boys?

4)From a class of 20 girls and 14 boys a group of 5 students must be selected to act as guides for the annual open house tours given to grade 8 students. How many different selections of 5 guides can be made ifDavid andLaura must be among those chosen?

5)How many positive odd integers of 5 different digits can be formed from the digits {1, 2, 3, 4, 5, 6, 7, 8, 9} if each integer is to be formed using 3 odd digits and 2 even digits?

6)In a history exam a student is asked to select any 5 paragraph questions from among eight paragraph questions presented. How many different selections can the student make if the order in which the questions is done is not important?

7)Using 3 letters from the word ARTICLE and 3 letters from the word SHOW, how many arrangements of six different letters are possible?

8)From a class of 9 boys and 10 girls a committee of 3 boys and 3 girls is to be chosen. In how many ways can this be done if Allan and Lindsey are either both on the committee or neither of them is on the committee?