# Difference between revisions of "2005 AMC 12B Problems/Problem 11"

The following problem is from both the 2005 AMC 12B #11 and 2005 AMC 10B #15, so both problems redirect to this page.

## Solution 2

Another way to do this problem is to use complementary counting, i.e. how many ways that the sum is less than 20. Now, you do not have to consider the 2 twenties, so you have 6 bills left. $\dbinom{6}{2} = \dfrac{6\times5}{2\times1} = 15$ ways. However, you counted the case when you have 2 tens, so you need to subtract 1, and you get 14. Finding the ways to get 20 or higher, you subtract 14 from 28 and get 14. So the answer is $\dfrac{14}{28} = \boxed{\mathrm{(D)}\ \dfrac{1}{2}}$.

## Solution 3

$P(\text{Get at least$ (Error compiling LaTeX. ! File ended while scanning use of \text@.)1$twenty})$ (Error compiling LaTeX. ! Extra }, or forgotten $.) =$1-\frac{\binom{6}{2}}{\binom{8}{2}$(Error compiling LaTeX. ! File ended while scanning use of \frac .)=\frac{28-15}{28}=\frac{13}{28}$

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