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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 ten tickets

$\begin{array}{1 1}(A)\;\large\frac{9990C_{10}}{10000C_{10}}\\(B)\;\large\frac{9990C_{3}}{10000C_{3}}\\(C)\;\large\frac{9990C_{5}}{10000C_{5}}\\(D)\;\text{None of these}\end{array}$

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 =$1000C_{10}$
Number of ways in which 10 tickets are without prize =$9990C_{10}$
Step 2:
Required probability =$\large\frac{9990C_{10}}{10000C_{10}}$
Hence (A) is the correct answer.