Question 11 In a lottery, person choses 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.]
Class X1 - Maths -Probability Page 405
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6 numbers out of 20 numbers can be selected in ²⁰C₆ ways .
hence, total number of possible outcome n( S ) = ²⁰C₆
only one combination of number is correct .
hence, number of favourable outcome n( E ) = 1
{ in only prize can be won }
∴ P( E ) = n( E )/n ( S )
= 1 / ²⁰C₆
= 1/{ 20!/6! × 14! }
= 6 × 5 × 4 × 3 × 2 /{ 20 × 19 × 18 × 17 × 16 × 15}
= 1/38760
P( E ) = 1/38760
hence, total number of possible outcome n( S ) = ²⁰C₆
only one combination of number is correct .
hence, number of favourable outcome n( E ) = 1
{ in only prize can be won }
∴ P( E ) = n( E )/n ( S )
= 1 / ²⁰C₆
= 1/{ 20!/6! × 14! }
= 6 × 5 × 4 × 3 × 2 /{ 20 × 19 × 18 × 17 × 16 × 15}
= 1/38760
P( E ) = 1/38760
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