n.阶乘
adj.【数】因数的；阶乘的；代理商的；工厂的

The factorial of 5 is calculated as 5*4*3*2*1, which equals 120.
阶乘计算为5*4*3*2*1，结果等于120。
In combinatorics, the concept of factorial is used to calculate permutations and combinations.
在组合数学中，阶乘的概念被用来计算排列和组合。
The probability of an event can often be determined using factorials when dealing with large numbers.
当处理大量数字时，事件的概率往往可以通过使用阶乘来确定。
Factorials grow very quickly; for instance, the factorial of 20 is over two million billion.
阶乘增长得非常快；例如，20的阶乘超过两百万亿。
The Gamma function is a generalization of the factorial function to real and complex numbers.
Γ函数是阶乘函数对实数和复数的一种推广。
To solve this problem, we need to find the factorial of the number of participants.
要解决这个问题，我们需要找到参与者人数的阶乘。
The factorial of a number is often used in statistical analysis to determine probabilities.
一个数的阶乘在统计分析中经常被用来确定概率。
The factorial notation is useful in simplifying expressions involving multiple multiplications.
阶乘符号在简化涉及多次乘法的表达式时很有用。
The teacher explained that the factorial of zero is defined as 1, not 0.
老师解释说，零的阶乘被定义为1，而不是0。
Using Stirling's approximation, we can estimate the value of large factorials without calculating them exactly.
利用斯特林近似，我们可以估算大阶乘的值，而无需精确计算它们。