Since 5 winning numbers are draw and there are exactly 2 winning numbers, the other 3 numbers chosen have to be incorrect.
The 2 numbers picked right, there are 5C2=10 different possibilities.
The other 3 numbers are just picked from the rest of the 32 numbers. Getting there are 32C3=4960 different possibilities.
For each set of 2 correct winning numbers, you could have the 4960 different losing numbers to match up to make a unique set. This meant that there are 4690*10=46900 different total possibilities.
Now the total different outcomes of how you can choose the numbers are 37C5=435897 outcomes.
Now the way to find probabilities is want/total
The want is 46900 and the total is 435897
Doing the division you get the number rounded to the nearest thousandths as 0.107 or in percent form as
10.759% chance of picking exactly 2 winning numbers.
This seems like a competition problem of some sort therefore I assume that you already know what combinations in form nCk and permutation in form nPk means.
Step-by-step explanation: To find the exponent, we look at the expression again and see how much of the same number or fraction is repeated. Since the main number is 1/9 and there are 3 fractions repeating it, the exponent is 
or 1/9 to the 3rd power.
<em>Down is a formula I made!</em>
Main number: 1/9
Repeating how many times: 3
Expression:
Therefore, 1/9 to the 3rd power is 1/729.
<em>Note: The questioner did not ask for the answer. I wanted to add it anyway for future reasons.</em>
B. 200 + (2 x $100) = t The student answer was not reasonable.
Because she spent $200 on the hotel which $189 rounded is $200.
$100 x 2 is 200 which is two $99's rounded (198)
Take 200 + 200 and you get 400.
For a bit of extra info she would have spent $400 rounded and $387 non-rounded.
