Question

State 3 different ways to end up with an answer of 1 when evaluating factorials.

a) 1!
b) 2!/2
c) 3!−2!
d) 4!/4!

Answer 1

Three methods to get a result of 1 using factorials are calculating 1!, dividing 2! by 2, and subtracting 2! from 3!, which are examples of factorial manipulations that can lead to the same result.

Step-by-step explanation:

There are three different ways to end up with an answer of 1 when evaluating factorials:

1. 1! which is the factorial of 1 and equals 1 by definition, as there's only one way to arrange one object.
2. 2!/2 is another way to achieve 1. Here's how it works: 2 factorial (2!) is 2 × 1, which equals 2. Dividing that by 2 (2!/2) gives us 1.
3. 3! − 2! is the third method. 3 factorial (3!) is 3 × 2 × 1, which equals 6, and 2 factorial (2!) is 2 × 1, which equals 2. Subtracting 2 from 6 (3! − 2!) equals 1.

These calculations demonstrate how factorial manipulations can lead to the same numerical result through different arithmetic operations.