Continuous random variables probability problem

Question

In $40$ calculations a student has made $7$ mistakes. If the teacher checks a randomly chosen set of five of these forty calculations, what is the probability the the teacher finds exactly two mistakes?

Not sure where to begin with this problem but I have attempted it. I Found the probability of finding a wrong question to be $\frac{7}{40}$, then I applied a binomial distribtion $(5C2)$($\frac{7}{40}$)$^2$(1-$\frac{7}{40}$)$^3$$=0.1719$

however the correct answer is $0.174$

Answer 1

The total number of different sets is $\binom{40}{5}=658008$

The number of different sets with $2$ mistakes is $\binom{40-7}{5-2}\cdot\binom{7}{2}=114576$

Hence the probability to choose a set with $2$ mistakes is $\frac{114576}{658008}\approx0.174$

Answer 2

Using the hypergeometric distribution which is for these type I get:

$$mistakes = 7$$

$$ trials = 5 $$

$$ picks = 2 \\$$

$$\frac{\binom{\text{mistakes}}{\text{picks}} \binom{40-\text{mistakes}}{\text{trials}-\text{picks}}}{\binom{40}{\text{trials}}}\approx.174125$$