In a lottery, a person chooses six different numbers at random from 1 to 20. If these 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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Solution

Number of ways in which 6 numbers can be chosen from 20 = $^{20} C_{6} = 38760$

Out of which only 1 is correct.

Hence, $p (E) = \frac{1}{38760}$

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In a lottery, a person chooses six different numbers at random from 1 to 20. If these 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 ?

Number of ways in which 6 numbers can be chosen from 20 = 20C6=38760 Out of which only 1 is correct. Hence, p(E)=138760

Number of ways in which 6 numbers can be chosen from 20 = $^{20} C_{6} = 38760$

Out of which only 1 is correct.

Hence, $p (E) = \frac{1}{38760}$