please answer ALL of the questions and please show your work.

1)How many positive integers between 3000 and 4000 can be made with the digits {3,4,6.9} if repetition of digits is allowed?

2)How many positive integers between 3000 and 4000 can be made with the digits {3,4,6.9} if repetition of digits is allowed?

3)In how many ways can all of the letters of the word HEXAGON be arranged if the arrangement must not end in a vowel?

4)How many 3-number combinations might a student have to try in order to open a lock if the numbers from 0 to 39 appear on the dial? Assume that the second number may be the same as the first (since the dial will be rotated in a different direction), but the third number must be at least 5 away from the second.

5)In how many ways can all of the letters of the word HEXAGON be arranged if the consonants and vowels must alternate in their positions in the word?

6)Using all of the digits {1,1,1,2,2,3,3}, how many positive seven-digit integers can be writtenthatare odd?

7)How many 6 digit numbers can be made using each of the digits {8,8,9,5,5,6} exactly once?

8)In how many ways might gold, silver, and bronze medals be awarded to 6 finalists in a 100 m sprint?

9)In how many ways can all of the letters of the word BOOKKEEPER be arranged ifthe vowels must all be together?

10)In how many ways can all of the letters of the word BOOKKEEPER be arranged ifthe vowels must all be together and the consonants must all be together?

11)In how many ways can all of the letters of the word BOOKKEEPER be arranged ifthe arrangement must start with B?

12)Using all of the digits {1,1,1,2,2,3,3}, how many positive seven-digit integers can be writtenthat begin and end in 1?

13)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 thatthere are no face cards? (jacks, kings and queens are the face cards)

14)Using letters from the word MANUSCRIPT, how many 4-letter arrangements consisting of 3 different consonants and 1 vowel can be formed if no letter is repeated?