CAIE IGCSE Additional Math 11 Permutation…nations

Covered syllabus points

11.1. Distinguish permutations and combinations 11.2. Use n! and nPr/nCr expressions 11.3. Solve arrangement and selection problems

[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

[Maximum number: 5]

A 6-character password is to be formed from the following characters.

Letters $\mathrm{b} \quad \mathrm{f} \quad \mathrm{g} \quad \mathrm{k} \quad \mathrm{m}$

Numbers 3259

Symbols * ! @

Each character can be used at most once in any 6-character password.

(a)

Find the number of 6-character passwords that can be formed if there are no further restrictions.

[ 1 ]

(b)

Find the number of 6-character passwords that can be formed if the password starts and ends with a symbol.

[ 2 ]

30240
M1 for $3\times10\times9\times8\times7\times2$ oe
A1

(c)

Find the number of 6-character passwords that can be formed if the password:
- starts with either a symbol and then a number, or a number and then a symbol and
- ends with 2 letters.

[ 2 ]

26880
B1 for a final answer of 13440, or M1 for $2\times3\times4\times8\times7\times5\times4$ oe
A1

[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 $3 n^{2}-19 n+20=0$ .

$\frac{n!}{(n-4)!}=\frac{(2 n)!}{6(2 n-3)!}$
Dep on previous B1
B1 for simplification of one side

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

All question bank results loaded

CAIE IGCSE Additional Math 11 Permutations and Combinations Topic Practice

Covered syllabus points

Question 1

Question 2

Question (a)

Question (b)

Question (c)

Question 3