In a certain lottery, 10,000 tickets are sold and ten equal prizes are awarded.

Total number of tickets sold = 10,000

Number prizes awarded = 10

(i) If we buy one ticket, then

$P$ (getting a prize) $=\frac{10}{10000}=\frac{1}{1000}$

$\therefore P($ not getting a prize $)=1-\frac{1}{1000}=\frac{999}{1000}$

(ii) If we buy two tickets, then

Number of tickets not awarded = 10,000 − 10 = 9990

$\mathrm{P}$ (not getting a prize) $=\frac{{ }^{9990} \mathrm{C}_{2}}{{ }^{10000} \mathrm{C}_{2}}$

(iii) If we buy 10 tickets, then

$P$ (not getting a prize) $=\frac{{ }^{9990} \mathrm{C}_{10}}{{ }^{10000} \mathrm{C}_{10}}$