Math Repository
about
topic
al
year
ly
Yearly
2009
P2 Q8
Topical
P&C
09 P2 Q8
2009 H2 Mathematics Paper 2 Question 8
Permutations and Combinations (P&C)
Answers
(i)
6720
{6720}
6720
(ii)
5040
{5040}
5040
(iii)
192
{192}
192
(iv)
480
{480}
480
Full solutions
(i)
Number of ways
=
8
!
3
!
=
6720
■
\begin{align*} &= \frac{8!}{3!} \\ &= 6720 \; \blacksquare \end{align*}
=
3
!
8
!
=
6720
■
(ii)
By the complement method, number of ways
E
E
E
L
V
A
T D
\textrm{E} \; \textrm{E} \; \textrm{E} \; \textrm{L} \; \textrm{V} \; \textrm{A} \; \boxed{\textrm{T } \textrm{D}}
E
E
E
L
V
A
T
D
=
6720
−
7
!
×
2
!
3
!
=
5040
■
\begin{align*} &= 6720 - \frac{7!\times2!}{3!} \\ &= 5040 \; \blacksquare \end{align*}
=
6720
−
3
!
7
!
×
2
!
=
5040
■
(iii)
C
V
C
V
C
V
C
V
V
C
V
C
V
C
V
C
\begin{gather*} \boxed{\textrm{C}} \; \textrm{V} \; \boxed{\textrm{C}} \; \textrm{V} \; \boxed{\textrm{C}} \; \textrm{V} \; \boxed{\textrm{C}} \; \textrm{V} \\ \textrm{V} \; \boxed{\textrm{C}} \; \textrm{V} \; \boxed{\textrm{C}} \; \textrm{V} \; \boxed{\textrm{C}} \; \textrm{V} \; \boxed{\textrm{C}} \\ \end{gather*}
C
V
C
V
C
V
C
V
V
C
V
C
V
C
V
C
Number of ways
=
4
!
×
4
!
3
!
×
2
=
192
■
\begin{align*} & = 4! \times \frac{4!}{3!} \times 2 \\ & = 192 \; \blacksquare \end{align*}
=
4
!
×
3
!
4
!
×
2
=
192
■
(iv)
E
_
_
_
E
_
_
E
E
_
_
E
_
_
_
E
_
E
_
_
E
_
_
E
E
_
_
E
_
_
E
_
\begin{gather*} \boxed{\textrm{E}} \; \_ \; \_ \; \_ \; \boxed{\textrm{E}} \; \_ \; \_ \; \boxed{\textrm{E}} \\ \boxed{\textrm{E}} \; \_ \; \_ \; \boxed{\textrm{E}} \; \_ \; \_ \; \_ \; \boxed{\textrm{E}} \\ \_ \; \boxed{\textrm{E}} \; \_ \; \_ \; \boxed{\textrm{E}} \; \_ \; \_ \; \boxed{\textrm{E}} \\ \boxed{\textrm{E}} \; \_ \; \_ \; \boxed{\textrm{E}} \; \_ \; \_ \; \boxed{\textrm{E}} \; \_ \\ \end{gather*}
E
_
_
_
E
_
_
E
E
_
_
E
_
_
_
E
_
E
_
_
E
_
_
E
E
_
_
E
_
_
E
_
Number of ways
=
5
!
×
4
=
480
■
\begin{align*} & = 5! \times 4 \\ & = 480 \; \blacksquare \end{align*}
=
5
!
×
4
=
480
■
Back to top ▲