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Factorial calculation

Calculating factorials including bracketed and divided

This math skill teaches how to calculate the value of a complex factorial expression that involves factorials in both the numerator and the denominator, including operations inside brackets and division between factorials. Key steps include expanding factorials, simplifying expressions, and cancelling terms to find the final value.

Learn factorial calculation

Teaching Transcript

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What is the value of this factorial expression?

We can start with the numerator and expand that factorial to 3 times 2 times 1

So our numerator, if we calculate that fully, is 6

Now let's simplify the brackets from 6 minus 3 to just 3

We can expand both factorials on the bottom

So our denominator is 2 times 6

If we cancel like terms top and bottom we're left with a final answer of one half

Skill Practice

Calculating factorials including bracketed and divided

Test your understanding of factorial calculation by practicing it! Work through the below exercises to use it in practice.