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How to Solve Factorial Expressions

A factorial of an integer "x" is written x! and represents the multiplication of all of the positive integers that proceed "x." For example, 4! equals 1 * 2 * 3 * 4. Note that the "0" is never included because "0" multiplied by anything equals "0." A factorial expression combines factorials through multiplication or division. The problem can be solved in a scientific calculator, which has a factorial key, or by hand using elimination techniques.

Instructions

- 1
  Solve a factorial expression containing factorials in the numerator and denominator by writing out the multiples out longhand then canceling out like terms. Multiply the remaining terms, simplifying where necessary, for the final answer.
- 2
  Solve the factorial expression 18! / 17!4!. Write out the factorials: (1 * 2 * 3 * 4...16 * 17 * 18) / (1 * 2 * 3 * 4...16 * 17)(1 * 2 * 3 * 4). Cancel out the common numbers from the 17 and 18: 18 / (1 * 2 * 3 * 4).
- 3
  Reduce the 18 using the 3 from the denominator: 6 / (1 * 2 * 4). Reduce the 6 using the 2 from the denominator: 3 / (1 * 4). Multiply the denominator for the final answer: 3/4.

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