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In a lottery, a person choses six different natural numbers at random from 1 to 20 and if these $\operatorname{six}$ numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?
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There are 20 natural numbers out of that 6 number may be chosen in ${ }^{20} C_6$ ways.
${ }^{20} C_6=\frac{20 \times 19 \times 18 \times 17 \times 16 \times 15}{1 \times 2 \times 3 \times 4 \times 5 \times 6}=38760$
There is only 1 favourable case which is being fixed by lottery committee.
Probability of winning the lottery $=\frac{1}{38760}$
${ }^{20} C_6=\frac{20 \times 19 \times 18 \times 17 \times 16 \times 15}{1 \times 2 \times 3 \times 4 \times 5 \times 6}=38760$
There is only 1 favourable case which is being fixed by lottery committee.
Probability of winning the lottery $=\frac{1}{38760}$
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