Quite some time ago there was a question in the two unit paper that involved
AP's and stacking logs? It became famous due to the confusion that was generated over the word "log". Does anyone know the year??
For the question
An eight letter word is constructed from EEEEEEGG. What is the prob it begins and ends with an E?
Total number of eight letter words=8!/(2!6!)=28
Number that start and end with an E 6!/(2!4!)=15
Method 2 Prob(start E)xProb(end...
But we almost always answer these questions via counting!!
An interesting point. If we ask the question
What is the probability that an 8 letter word constructed from the 8 characters
EEEEEEGG begins and ends with an E?
then both methods agree!
Why does the usual method of...
!!!!!!!!!!!!!!!!!!!!!! But the answer is NOT 4/11 !!!!!!!!!!!!!!!!!!!!!!!
Imagine that I change the question so that the eight characters are replaced by 1000 E's and 2 G's.
You will still get 4/11 with the above attack but the correct answer is clearly very close to 1.
Here's a strange one!
a) A 4 letter word is to be constructed using the 8 characters EEEEEEGG.
In how many ways can this be done?
b) How many of the words in a) begin and end with an E?
c) What is the probability that a 4 letter word constructed from the 8 characters
Here is a spooky little question for everyone preparing for the trials.
In how many different ways can six identical black marbles and six idententical white marbles be arranged in a circle?
Think carefully abvout your answer
suppose that |z-a|=r (z lies on a circle of radius r centred at a) and |a| is not equal to r (circle does not contain 0)
the locus of 1/z is also a circle.
Its trivial of course when a=0
I'm after a variety of different proofs (no insane determinant...