! is the symbol for factorial, which means the product of the whole numbers less than the given number.

Thus, .

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it. So, can also be written as:

To make this easier for ourselves, we can cancel out the numbers that appear on both the top and bottom:

Simplifying this equation we notice that the 3's, 2's, and 1's cancel so

Alternative Solution

! is the symbol for factorial, which means the product of the whole numbers less than the given number.

Thus, .

The factorial sign (!) just tells us to multiply that number by every integer that leads up to it. So, can also be written as:

To make this easier for ourselves, we can cancel out the numbers that appear on both the top and bottom:

By definition, .

By definition, .

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, .

Rather than do all of the math involved for , notice that is the same as

From here, the 's cancel out, leaving us with .

Remember a number followed by a ! is a factorial. A factorial is the product of the given number and all of the numbers smaller than it down to zero. For example, .

Rather than do all of the math involved for , notice that is the same as

From here, the 's cancel out, leaving us with .