NCERT Class XI Mathematics - Probability - Solutions

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Question : 34
Total: 54
In a lottery, a person chosen 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]
Solution:  
An experiment consists of a lottery, a person chose six different natural numbers at random from 1 to 20.
∴ Sample points =
20
C6
=
20×19×18×17×16×15
1×2×3×4×5×6
= 38760
Let E be the event that chosen six numbers match with the six numbers already fixed by the lottery committee, i.e. Winning the prize in the game
n (E) =
6
C6
= 1
∴ P (E) =
n(E)
n(S)
=
1
38760

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