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Home » 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?
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?
CBSE | Class 11 | Exercise 31A | Maths | Probability Distribution | RS Aggarwal
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?

Answer : All numbers are different (given in question), this will be the same as picking r different objects from n objects which is ncr

Here, n= 20 and r = 6(as we have to pick 6 different objects from 20 objects)

Now we shall calculate the value of 20C6  as nCr

i.e. 20C6 = 38760

Therefore, 38760 cases are possible, and in that only one them has prize, i.e. total no.of desired outcome is 1

As we know,

Probability of occurrence of an event

Therefore, the probability of winning a prize is

1/38760
Conclusion: Probability of winning the prize in the game is 1/38760

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