These have to do with combinations and permutations please answer ALL of the questions and please show your work so it is easier to understand.

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)How many different selections of 2 good eggs can be made from a carton containing one dozen eggs,if the cartoncontains 4 rotten eggs and 8 good eggs?

5)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?

6)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?

7)How many 10-card hands can be dealt from a standard deck of 52 cardsif 8are redand 2 are black?

8)A box contains 4 red marbles, 3 blue marbles, and 5 yellow marbles. In how many ways can one select a set of 5 marbles from the box such thatnone of themare blue?

9)A small class consists of 5 boys and 7 girls. How many groups can be selected from this class that consist of4boys and4 girls?

10)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 ifthere are no restrictions?

11)In five-card poker in how many ways could you be dealt 4 of a kind?

12)A box contains 4 red marbles, 3 blue marbles, and 5 yellow marbles. In how many ways can one select a set of 5 marbles from the box such that2 are red, 1 is blue,and2 are yellow?

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

14)There are 26 red cards and 26 black cards in a standard deck of 52 cards. The red cards are divided into two suits (hearts and diamonds) and the black cards are divided into two suits (clubs and spades). The 13 cards within each suit are known as the 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, king, queen, and ace of that particular suit. In the game of 5-card poker, each player is dealt 5 cards. How many 5-card hands can be dealt such thatallcards are black?

15)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 ifAllan must be on the committee but Lindsey must not be on the committee?

16)How many 10-card hands can be dealt from a standard deck of 52 cards that consist ofall black cards?

17)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 ifno girls are chosen?

18)How many different selections of 2 eggs can be made from a carton containing one dozen eggs?

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

20)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 ifboth boys andgirls are represented?

21)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?