1) Write a program to calculate n! 2) ``Lucky 7'' is defined as when the addition of both dice equals 7 in one throw. A die [dice is plural] has 6 sides numbered 1-6. Write a program to count the number of throws it takes two dice to get 100 Lucky 7's. [Hint: you must use the rand() function to simulate dice throws.] Use the following headers: #include #include #include 3) Next, write a program that will print the upper left corner of numbers given a number by the user: Give me a number :> 10 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 5 6 7 8 9 10 6 7 8 9 10 7 8 9 10 8 9 10 9 10 10 Extra: Try to do the same with the other four corners and try to keep the number's position: Example: 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 1 2 3 1 2 1 1 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 5 6 7 8 9 10 6 7 8 9 10 7 8 9 10 8 9 10 9 10 10 10 9 10 8 9 10 7 8 9 10 6 7 8 9 10 5 6 7 8 9 10 4 5 6 7 8 9 10 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 1 1 2 1 2 3 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 10