According to the Birthday Paradox, if there are $676$ possible outcomes of an event, how many items need to be randomly chosen to have a $50\%$ chance of a collision?

a$.20$

B$.26$

$P(n)=1-\frac{\text{u}\text{n}\text{i}\text{q}\text{u}\text{e}\text{o}\text{u}\text{t}\text{c}\text{o}\text{n}\text{e}\text{s}}{\text{t}\text{o}\text{t}\text{e}\text{d}\text{o}\text{l}\text{o}\text{u}\text{t}\text{o}\text{r}\text{n}\text{e}\text{s}}$

c$.124$

$Z$ the smallest $n$ for $P(n)0\mathrm{.}5$

d$.3380\mathrm{.}51-(\frac{676}{676}{)}^{n}1$