A. Solve the following. Remember that the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. 0! is defined as 1.
1: What is 7!?
2: Calculate 10!.
3: Simplify 11!/8!
4: Evaluate 8!/(4!5).
5: Solve for n: n! = 1,440
6: What is the value of 7!/(3!5!)?7: Simplify (n+3)!/n!.
8: Find the value of 13!/(11!3!).
9: If n!/(n-2)! = 20, find n.
10: What is the value of 1!?
B. Solve the following Factorial word problems:
1: A foreman wants to arrange his 7 carpenters in a row for a photograph. How many different arrangements are possible?
2: How many ways can you arrange the letters in the word "VAST"?
3: A confectionery store offers 8 different candies. If a customer orders 4 kinds of candies6, how many different combinations are possible, assuming the order doesn't matter? (Note: This is a combination problem, not a direct factorial application, but it uses factorials in its solution)
4: A bookshelf has space for 7 books. If you have 9 books, how many ways can you arrange 7 of them on the shelf?
5: How many ways are there to arrange the letters of the word "RABBIT"? (Consider that the letter B is repeated)
6: A restaurant offers 6 different dishes. How many different rice meal can be made with 3 dishes, if the order of rice meal doesn't matter? (Combination)
7: Eleven people are running a race. How many different ways can the first three places be awarded (gold, silver, bronze)?
8: A password must be 5 characters long, using only the digits 0-9. How many possible passwords are there if repetition is allowed?
9: A group has 13 members. How many ways can they elect a president, vice-president, and treasurer?
10: How many different ways can 8 distinct books be arranged on a shelf?
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