CAIE IGCSE Additional Math 11.2 nPr and nCr expressions

Use this nPr and nCr page to expand notation into factorial form, simplify equations and solve for the unknown value of n.

Exam points

Convert nPr and nCr expressions into factorial form before simplifying.
Solve equations involving combination terms such as nC3 or nC4 after expansion.
Solve equations involving permutations such as nP5 and related factorial expressions.

[Maximum number: 4]

The number of permutations of n items taken 4 at a time is equal to $\frac{1}{6} \times$ the number of permutations of 2 n items taken 3 at a time.

Show that n satisfies the equation $3 n^{2}-19 n+20=0$ .

$\frac{n!}{(n-4)!}=\frac{(2 n)!}{6(2 n-3)!}$

B1

Dep on previous B1
B1 for simplification of one side

e.g. 3(n-2)(n-3)=2(2 n-1)
$3 n^{2}-19 n+20=0 \mathbf{A G}$

B1

Dep on all previous B marks

With sufficient detail shown

\begin{array}{r} n(n-1)(n-2)(n-3)= \frac{2 n(2 n-1)(2 n-2)}{6} \end{array}

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11.2. Use n! and nPr/nCr expressions question 1