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Question
In a lottery, person chooses six different natural numbers at random from 1 to 20, and 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? [Hint: order of the numbers is not important.]
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Solution
Ways to choose 6 numbers from natural numbers from 1 to 20 = `""^20"C"_6`
= `(20 xx 19 xx 18 xx 17 xx 16 xx 15)/(1 xx 2 xx 3 xx 4 xx 5 xx 6)`
= 38760
There is only one favourable outcome.
So the probability of winning the lottery = `1/38760`.
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