Mr. Magico is a greater believer in this number:
$$2^{50}=1,125,899,906,842,624$$
He also like to play cards, although he isn't fussy about the size of his deck, and nor does he care how many cards he pulls.
He wishes to find $n,k$ such that:
$$\binom{n}{k}\approx 2^{50}$$
and wants $n$ as small as possible, but also a very small error margin. $2^{50}$ cards gives $100\%$ accuracy, but is a very large pack of cards, probably too large for even Mr. Magico to carry around in his pocket!
With this in mind, we shall impose an upper limit of $n\le500$, although $n\le100$ would be better for Mr. Magico's posture!
What is Mr. Magico's ideal pack of cards, and how many cards should he pull?
For a start $\dbinom{78}{14}=1,023,729,916,348,425$, an error of $\sim0.909$.