Hello forumites

Ten pairs of shoes are in a closet. Four shoes are selected at random. Author wants me to find the probability that there will be at least one pairs of shoes among the four shoes selected.

Solution:-

Four shoes can be selected out of 10 pairs (20 number) in $\binom{20}{4}$ ways. Now we want to find the probability that there will be at least one pair of shoes among the four shoes selected which is equal to the probability that remains after deducting the probability of no pairs of shoes among the four shoes selected from the total probability.. So it is $1-\frac{\binom{10}{4}}{\binom{20}{4}}=0.956656$

But answer provided is $\frac{99}{323}=\frac{\binom{55}{2}}{\binom{20}{4} }$ Now which is wrong?