Questions on factorial can appear in H2 math binomial expansion, partial fractions, method of difference, mathematical induction and probability. Knowing how to simplify and manipulate factorials are crucial to doing well.

Two commonly used techniques

1. Replace n! with n(n-1)!

2. Multiply by k/k  or k! / k!

Example 1

factorial 1

 Example 2 

Solve the inequality

(r+1)!(17-r)!(9-r)!(r+3)! > r!(18-r)!(10-r)!(r+2)!

(A level 2011, P2 Q11)

(r+1)r!(17-r)!(9-r)!(r+3)(r+2)! > r!(18-r)(17-r)!(10-r)(9-r)!(r+2)!

(r+1)(r+3)> (18-r)(10-r)

32r > 177

r > 5.53

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