SOLUTION: A state lottery requires you to pick 6 different numbers from 1 to 40 to win $1,000,000. A) what is the probability of winning if order is not important? B) If you pick 5 of the 6

 
Calculate the numerator:
There is only one winning combination.  So the numerator of the 
desired probability is 1.

Calculate the denominator:
There are "40 numbers, choose 6", or 40C6 possible combinations.
So the denominator of the desired probability is 40C6.

So the probability is 

Suppose the winning 6 numbers were, say,

   6,  13,  26,  28,  31,  35

Calculate the numerator:

There are "6 numbers, choose 5" or 6C5 ways to pick 5 correctly. 
AND
you must also pick 1 wrong number.  That wrong number has to be
different from any of the 6 correct numbers, and so there are
40-6 or 34 wrong numbers you could have picked.  That's 34 wrong
numbers, choose 1 or 34C1. Since AND means to multiply, the
numerator is 

The denominator is the same 3838380 as in part (A)

So the desired probability is 

However that's just the probability of winning the $10000.

The words "probability of winning" could be taken as the
probability of winning either $1,000,000 OR $10,000. So

P(winning $1,000,000 OR winning $10,000) and since 
"OR" means "ADD", we add the probability found in part A,

so the correct answer is ,
the probability of winning a million or ten thousand.

Edwin