All solutions here are suggested. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions
Numerical Answers (workings/explanations are after the numerical answers. Click to expand.)
Question 1: 
; 6 cars, 7 trains and 10 boats.
Question 2: 
Question 3: 
Question 4: 
Question 5: 
Question 6: 
Question 7: 
Question 8: 
Question 9: 
Question 10: 
—(1)
—(2)
—(3)
be the number of cars, trains, and boats that Sam has, where 
and 
, then 
must be divisible by 
for 
to be an integer. 
, then 
. Using GC, we can find 
.
against 
, 
and 
. Thus, Sam has 6 cars, 7 trains and 10 boats.
![\vec{OR} = \frac{1}{3} \bigg[ 7 \vec{OQ} - 4 \vec{OP} \bigg]](http://theculture.sg/wp-content/ql-cache/quicklatex.com-f66e681b67f9b8a9b39673198a23bf27_l3.png "Rendered by QuickLaTeX.com")
, where 
or 
and 
is an odd function, then 
, for all 
is symmetrical at every vertical lines 
units apart.
for 
, where 
and 
seconds
s
.![\frac{12!}{[12 - (n-1)]!} \times \frac{[15 - (n-1)]!}{15!} \frac{3}{16 - n} = \frac{36}{455}](http://theculture.sg/wp-content/ql-cache/quicklatex.com-079509315a02cefc33108c577d3c17c8_l3.png "Rendered by QuickLaTeX.com")
ways
ways
ways
denote the number of days with more than one faulty refrigerator, out of five days. 
denote the number of faulty refrigerator, out of 450 refrigerators.
Comments
Hi Mr Teng,
It would be easier to use guess-and-check approach for P2/Q1(b).
(6, 7, 8) gives 103
(6, 7, 9) gives 108
(6, 7, 10) gives 113
Thank you.
Best regards