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NSWMaths Extension 1Quick questions
Combinatorics (ME-A1)
Quick questions on Factorial notation: definition, the convention 0! = 1, the recursive rule, and simplifying factorial fractions
3short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What are unrolling to simplify factorial fractions?Show answer
Almost every exam manipulation of factorials is a fraction in which most of the product cancels. The method is always the same: take the larger factorial and unroll it, one factor at a time, until you reach the smaller factorial, which then cancels top and bottom. You never need to evaluate either factorial in full.
What is combining factorial fractions over a common factorial?Show answer
When two factorial fractions are added or subtracted, do not find some huge common denominator by multiplying the factorials together. Instead use the recursive rule to write the smaller factorial in terms of the larger one, so the larger factorial is already the common denominator.
What is trailing zeroes of a factorial?Show answer
A neat application that NESA likes, because it tests understanding rather than button-pushing, is counting how many zeroes a factorial ends in. You cannot do it on a calculator beyond about , since the display runs out of digits, but a short argument settles it exactly.
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