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# In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded.What is the probability of not getting a prize if you buy one ticket

$\begin{array}{1 1}(A)\;\large\frac{999}{1000}\\(B)\;\large\frac{909}{1000}\\(C)\;\large\frac{979}{1000}\\(D)\;\large\frac{989}{1000}\end{array}$

Toolbox:
• $nC_r=\large\frac{n!}{r!(n-r)!}$
• Required probability=$\large\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}=\frac{n(E)}{n(S)}$
Step 1:
Given total tickets =10,000
Out of which 10 tickets have prizes 9990 are blank
Total number of outcomes =1 ticket from 10,000 can be selected $10000C_1$ ways
Number of ways in which 1 ticket is without prize =$9990C_1$
Step 2:
$\therefore$ Required probability =$\large\frac{n(E)}{n(S)}$
$\Rightarrow \large\frac{9990C_1}{10000C_1}$
$\Rightarrow \large\frac{9990}{10000}$
$\Rightarrow \large\frac{999}{1000}$
Hence (A) is the correct answer.