An FM radio channel has a repository of $10$ songs. Each day, the channel plays $3$ distinct songs that are chosen randomly from the repository.
Mary decides to tune in to the radio channel on the weekend after her exams. What is the probability that no song gets repeated during these $2$ days?
- $\begin{pmatrix} 10\\ 3 \end{pmatrix}^{2}*\begin{pmatrix} 10\\ 6 \end{pmatrix}^{-1}$
- $\begin{pmatrix} 10\\ 6 \end{pmatrix}*\begin{pmatrix} 10\\ 3 \end{pmatrix}^{-2}$
- $\begin{pmatrix} 10\\ 3 \end{pmatrix}*\begin{pmatrix} 7\\ 3 \end{pmatrix}*\begin{pmatrix} 10\\ 3 \end{pmatrix}^{-2}$
- $\begin{pmatrix} 10\\ 3 \end{pmatrix}*\begin{pmatrix} 7\\ 3 \end{pmatrix}*\begin{pmatrix} 10\\ 6 \end{pmatrix}^{-1}$