IN MATH: 1. n. the product of a natural number n, and every natural number smaller than it. It is written as n! and factorial is also defined for 0, written 0!, and defined to be 1. 2. a mathematical function which produces the product of a natural number and each natural number smaller than it. . EX. To compute the value of 6!, find the product of 6 and 5!, 6(5!).

- 0! = 1
- 1! = 1
- 2! = 2(1!) = 1 (1) = 2
- 3! = 3(2!) = 3(2)(1) = 6
- 4! = 4(3!) = 4(3)(2)(1) = 24
- 5! = 5(4!) = 5(4)(3)(2)(1) = 120
- n! = n(n-1)! = n(n-1)(n-2) ...(4)(3)(2)(1)

IN ENGLISH: as defined above.

APPLICATION: See Basic Probability.

1. A club has 4 members and wishes to elect a president, vice president, secretary, and treasurer. In how many ways can this be done?

2. A club has n members and wishes each member to hold an elected office, beginning with the president, vice president, secretary, and treasurer. In how many ways can this be done?

3. A club has 4 members and wishes to form a committee of 2 member. In how many ways can this be done?

4. A club has n members and wishes to form a committee of r member. In how many ways can this be done?

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