MrGenius

Exactly.  Thanks CPhill for having the courage to rewrite the whole number (You deserved a brownie for this)

This was the correct answer in the American short scale. In the old British long scale, it would have been written like this :

«Thirty-four quadriliard, two hundred and eighty-six quadrillion, two hundred and twenty-seven trilliard, five hundred and seventy-four trillion, three hundred and eighty-seven billiard, fourty-five billion, four hundred and eighty-one milliard, six hundred and ninety-one million, three hundred and eighty-six thousand eight hundred and seventy-five».

The formula to calculate this is :

\(\binom{N}{p}=\frac{N!}{(N-p)!\times p!}\)

Where N is the total number of numbers, and p the number of numbers the player choose.

Now, let's call Q the number of possible draws to the LOTO. Then Q is equal to:\(Q=\binom{49}{5}\times \binom{10}{1}=\frac{49!}{44!\times 5!}\times \frac{10!}{9!\times 1!}=19\: 068\: 840\)

So there are 19 068 840 possible lotery draws.

$$\\m=\rho \times V=2.703 \times 2.5=6.7575 \textup{ kg}=6.7575\times 10^3 \textup{g}
\\\\M_{KMnO_4}=M_K+M_{Mn}+4\times M_O
\\=39.098+54.936+(4\times 15.999)
\\=158.03\textup{ g}\cdot \textup{mol}^{-1}
\\\\n=\frac{m}{M}=\frac{6.7575\times 10^3}{158.03}=\textcolor[rgb]{0,0,1}{42.7609\textup{ mol}}$$

The American billion is 1,000,000,000; this was called, in Britain, until 1974, a thousand million or, more occasionnally, a milliard.

See Numberphile's video: