DEGREES

If we select $5$ degrees without replacement, what is the probability that at least one of them will be a Doctoral degree?

$1-(\frac{237}{313}*\frac{237}{313}*\frac{237}{313}*\frac{237}{313}*\frac{237}{313})$

$1-(\frac{76}{313}*\frac{76}{313}*\frac{76}{313}*\frac{76}{313}*\frac{76}{313})$

$1-(\frac{237}{313}**\frac{236}{312}**\frac{235}{311}**\frac{234}{310}**\frac{233}{309})$

$\frac{76}{313}*\frac{76}{313}*\frac{76}{313}*\frac{76}{313}*\frac{76}{313}$

$\frac{76}{313}*\frac{75}{312}*\frac{74}{311}*\frac{73}{310}*\frac{72}{309}$

$\frac{237}{313}*\frac{236}{312}*\frac{235}{311}*\frac{234}{310}*233/309$

$\frac{237}{313}*\frac{237}{313}*\frac{237}{313}*\frac{237}{313}*\frac{237}{313}$

$1-(\frac{76}{313}*\frac{75}{312}*\frac{74}{311}*\frac{73}{310}*\frac{72}{309})$