These Ten-Year-Series (TYS) worked solutions with video explanations for 2017 A Level H2 Mathematics H1 Question 8 [Modified] are suggested by Mr Gan. For any comments or suggestions please contact us at support@timganmath.edu.sg.
2017 A Level H2 Math H1 Question Q8 [Modified]
A code consists of $6$ characters. The first $3$ characters of the code consists of $3$ digits chosen from $\left\{ 1,\,\,2,\,\,3,\,\,4,\,\,5,\,\,6 \right\}$.
The last $3$ characters of the code consists of $3$ letters chosen from $\left\{ A,\,\,B,\,\,C,\,\,D,\,\,E,\,\,F,\,\,G,\,\,H \right\}$.
(i)
How many codes can be formed if repetitions are not allowed?
(i) How many codes can be formed if repetitions are not allowed?
Now suppose that repetitions are allowed. Find the number of codes that
(ii)
contain the digit $5$ exactly once and the letter $H$ exactly twice.
(ii) contain the digit $5$ exactly once and the letter $H$ exactly twice.
(iii)
have $2$ as its first character or $H$ as its sixth character, but not both.
(iii) have $2$ as its first character or $H$ as its sixth character, but not both.
Suggested Video Solutions
Suggested Handwritten Solutions
![N2017 H1 Q8 [Modified]](https://timganmath.b-cdn.net/wp-content/uploads/N2017-H1-Q8-Modified-i.png)
![N2017 H1 Q8 [Modified]](https://timganmath.b-cdn.net/wp-content/uploads/N2017-H1-Q8-Modified-ii.png)
![N2017 H1 Q8 [Modified]](https://timganmath.b-cdn.net/wp-content/uploads/N2017-H1-Q8-Modified-iii.png)
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