FTCE General Knowledge Math Practice Test

What does the symbol 'n!' represent in mathematics?

1. The nth term in a sequence

2. The factorial of n

3. The number of combinations of n items

4. The nth root of n

The correct answer is: The factorial of n

The symbol 'n!' in mathematics represents the factorial of n. The factorial of a non-negative integer n is defined as the product of all positive integers from 1 to n. Specifically, it can be expressed as: n! = n × (n - 1) × (n - 2) × ... × 3 × 2 × 1 For instance, if n = 5, then 5! = 5 × 4 × 3 × 2 × 1 = 120. This concept is particularly relevant in combinatorics, probability, and various areas of mathematics where counting arrangements or permutations is necessary. Factorials serve as a foundation for calculating combinations and permutations by determining how many different ways you can arrange or select a subset of items from a larger set. While the other choices involve mathematical concepts, they do not accurately define the symbol 'n!'. The nth term in a sequence pertains to the specific element in a defined sequence, combinations involve a different notation and context (often represented as nCr), and the nth root refers to a radical expression rather than a factorial computation.