CAIE IGCSE Additional Math 11.2 Use N and Npr Ncr Expressions Questions

Practise Cambridge IGCSE Additional Mathematics by expanding nPr and nCr expressions, solving for n and checking valid domains.

Exam points

Expand permutations and combinations into factorial products or consecutive factors.
Form and solve the resulting algebraic equation for the integer parameter n.
Check domain constraints and reject non-integer or invalid parameter values.

[Maximum number: 3]

the equation $(n-4)^{n+1} C_{5}={ }^{n+2} C_{7}$ .

$\frac{(n-4)(n+1)!}{(n-4)!5!}=\frac{(n+2)!}{(n-5)!7!}$

leading to
$\times 6=n+2$ B1 for $7 \times 6$ or 42 seen as a result of simplification of the numerical factorials

B1 for n+2 seen as a result of simplification of the algebraic factorials
n=40 B1

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CAIE IGCSE Additional Math 11.2 Use N and Npr Ncr Expressions Questions question 1