E1 and E2 are two different events. The first event can happen in m1 different ways and the second event can happen in m2 different ways. M1 x m2 is the number ways that two events can occur.
For example if we were to find the total different combinations of telephone numbers for each area code, we see that there are eight different events. (Important to note that the first digit cannot be 0 or 1, thus giving us eight ways event one can occur).
8 x 10 x 10 x10x10x10x10. = 8,000,000.
Permutation (order matters)
A permutation of x number of elements is an ordering of elements.
For instance, if 4 people were in a line, we could be asked how many different ways could they line up.
In this case order matters.
4 different people can take the first spot, then 3 different people can take the second part since somebody already took the first spot. And so on.
4! = 24 different ways.
Let's also say that 8 track runners ran in a race. How many different combinations of runners can get 1st, second, and third.
In this instance, we use the equation nPr= n!/(n-r)!
Thus 8P3=8!/(8-3)! =336
Combinations (order doesn't matter)
The number of combinations taken r at a time is denoted by
nCr=n!/(n-r)!r!
Let's say we were choosing 4 marbles from a bag of 7 marbles. How many different combinations of 4 can we get?
7C4=7!/(7-4)!4! = 35 different ways.
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