Consider the following 3 cases:
Problem
A bag contains 10 orange-flavoured, 14 strawberry-flavoured and 16 cherry-flavoured sweets which are of identical shapes and sizes. Benny selects a sweet at random from the bag. If it is not cherry-flavoured, he replaces it and selects another sweet at random. He repeats the process until he obtain a cherry-flavoured sweet. Calculate the probability that
i) the first sweet selected is strawberry-flavoured and the fourth sweet is orange-flavoured;
ii) he selects an even number of sweets
Solution
Is 
?
The answer is no. Correct answer is 
See the following example how this concept is applied in H2 math
Example 1
Differentiate 
with respect to x
Therefore
Ans: -1 if sin x > 0, 1 if sin x < 0
Example 2
Use implicit differentiation to differentiate the following with respect to x:
y=x(x+1)(x+2)(x+3)(x+4)(x+5)
Solution
ln y= lnx+ln(x+1)+ln(x+2)+ln(x+3)+ln(x+4)+ln(x+5)
In how many ways can 9 balls of which 4 are red, 4 are white and 1 black be arranged in a line so that no red ball is next to the black?
Answer: 175
Solution
Case 1: 1st ball is black in the whole row of 9 balls
Then the 2nd ball must be white. The rest of the 4 red and 3 white balls can be arranged in 
= 35 ways
Case 2: last ball is black
Then the 2nd last ball must be white. The rest of the 4 red and 3 white balls can be arranged in = 35 ways
Case 3: Black ball is not the 1st or last ball
Then the black ball must be between 2 white balls. Consider WBW as one unit. Together with 4 red balls and 2 white balls, these can arranged in 
= 105 ways
Using the addition principle, total number of ways = 35+35+105= 175
JC A Level H2 Math Tuition Singapore 
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