Factorials - Math

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

This is a factorial question. The formula for factorials is .

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for in the numerator. Multiply those together to get 720.

Thus, since the remaining terms cancel out. 56 is the simplified result.

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 .

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:

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

Thus, .

By definition, .

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

Thus, .

By definition, .

This is a factorial question. The formula for factorials is .

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

Alternative Solution

This expression can be simplified because all terms in the expression for 8! are also found in the expression for 10!. By writing the expression below, we are able to cancel 8!.

The cancels out all of except for the parts higher than 4, this leaves a 6 and a 5 left to multilpy

Both the numerator and denominator are factorials. If you expanded both, everything would cancel out except for in the numerator. Multiply those together to get 720.

Thus, since the remaining terms cancel out. 56 is the simplified result.

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 .

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: