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The above solutions had been worked out by Mr Teng.
Errata:
For qn 3(I) line 7, the denominator of the third derivative of f(x) should be of power 4 instead of 2.
For qn 4(I), was some scanning error. The answer is 40.4.
For qn11(III), I made a terrible mistake and forgot the third case for which exactly three letters same AND two digits same. The permutation for that will be (26×9).
11(iv) I made the mistake of double counting and arranged after using the permute function. The following is the full solutions
Case 1: Exactly one vowel and 2 different consonants and exactly one even digit
(5C1)(21C2)(3!)(4C1)(5C1)(2!) =252000
Case 2: Exactly one vowel and 2 same consonants and exactly one even digit
(5C1)(21C1)(3!/2!)(4C1)(5C1)(
P(exactly one vowel & exactly one even digit) = (252000+12600)/(26^3*9^2) = 0.186 (3SF)
Disclaimer: We welcome fair comments and discussion. The answers were rushed out and done while Mr Teng was in between classes too. So there are errors definitely, so many thanks for all who point them out. 🙂
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