can you please help with these questions they have to do with the fundamental counting principal. please answer ALL of the questions and show your work so it is easier to understand.

1)A schoolhas 4 entrances and 9 exits (the 4 entrances and an additional 5 crash doors). In how many ways can a student enter the school and leave by a different door?

2)Using the digits {1,2,5,6,7,9} and not allowing repetition of digits, how many positive three-digit integers can be made that arelarger than 500?

3)How many positive two-digit integers can be made from the digits {2,4,5,8} if digits may not be repeated?

4)Slot machines have 3 dials with 20 symbols on each dial as shown in the chart below.In how many ways can one get 3 bars? Just place the number in the answer box, a statement is not necessary.

Symbol	Dial 1	Dial 2	Dial 3
Bar	2	1	1
Bell	1	8	7
Cherry	2	7	0
Lemon	0	0	5
Orange	8	2	4
Plum	7	2	3
Total	20	20	20

5)Andrea, Brian, Carol, David, Emmalee, Floyd, and Gloria are to stand in a line for a photograph. If they each face the photographer, in how many ways can they be arranged ifthe boys must be together on the left and the girls must be together on the right?

6)If each one of a set of septuplets wants to attend a different high school, in how many ways can they choose their schools if they live in a city with 11 high schools?

7)Using the digits {1,2,5,6,7,9} and not allowing repetition of digits, how many positive three-digit integers can be made that areodd?

8)How many 7-digit phone numbers can be made if the first digit cannot be a 0?

9)Positive integers like 393, 5445, 78987, 444444 are called palindromes-they are unchanged when their digits are written in reverse order. How many five-digit palindromes are there?

10)Assume that a Saskatchewan license plate consists of 3 letters followed by 3 digits (the first of which cannot be 0). How many vehicles might the police have to track down in order to find the getaway vehicle used in a bank robbery if a witness can only remember the first two letters and the last digit of the license plate?

11)How many positive four-digit integers can be formed thatdo not contain the digit 3?

12)In how many ways can all of the letters of the word HEXAGON be arranged if the middle letter in the arrangement must be X?

13)A student is takingPre-Calculus 20, Chemistry 20, History 20, English 20, and French 20. If the school has 5 math teachers, 3 chemistry teachers, 4 history teachers, 8 English teachers, and 2 French teachers, how many teacher assignments could the student receive?

14)How many 7-digit phone numbers can be made if the first three digits can only be 3's or 4's but there are no restrictions on the last four digits?

15)Andrew's mother always makes his lunch for him. She packs one brown-bread sandwich, one white-bread sandwich, one fruit item, and one dessert item. Andrew likes ham, cheese, salami, chicken, turkey, and jam as sandwich fillings. He likes apples, grapes, bananas, and pears, and he likes Oreo cookies, chocolate cake, fudge, butterscotch pudding, and O'Henry clusters for dessert. How many lunches can Andrew have if his mother puts a different filling in each sandwich?

16)How many boy-girl dancing couples could be formed if 85 boys and 102 girls attend a school dance?

17)Using the digits {1,2,5,6,7,9} and not allowing repetition of digits, how many positive three-digit integers can be made that aredivisible by5?

18)S7H 3V8 is a typical Saskatchewan postal code. How many postal codes can be formed that begin with S if any digit may be used in the digit positions and any letter may be used in the other letter positions?

19)How many positive four-digit integers can be formed if there are no restrictions?

20)In how many ways can three door prizes, one each of $100, $50, and $25, be given out if 30 people have entered the contest and no one can win more than one prize?

21)In how many ways can a 10-question true-false test be answered if each of the questions is attempted?

22)How many positive four-digit integers can be formed that areodd?

23)How many different batting orders can a baseball coach form if all 9 players must bat?

24)Andrea, Brian, Carol, David, Emmalee, Floyd, and Gloria are to stand in a line for a photograph. If they each face the photographer, in how many ways can they be arranged if Andrea and Brian muststand beside one another?

25)Andrea, Brian, Carol, David, Emmalee, Floyd, and Gloria are to stand in a line for a photograph. If they each face the photographer, in how many ways can they be arranged ifthe boys must be together?

26)In how many ways can all of the letters of the word HEXAGON be arranged if the arrangement must start with H and end in N?