In a lottery, a person choses six different natural numbers at random from1 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 games? [Hint: order of the numbers is not important.]
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Answer:
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Step-by-step explanation:
Total number of ways in which one can choose six different numbers from 1 to 20 is ²⁰C₆
The ⁿCᵣ formula is, ⁿCᵣ = (n!) / [ (n-r)! r! ]. From this,
²⁰C₆ = (20)! / [(6)!(20 - 6)!]
= 20 × 19 × 18 × 17 × 16 × 15 × (14)! / [(6)!(14)!]
= (20 × 19 × 18 × 17 × 16 × 15) / (1 × 2 × 3 × 4 × 5 × 6)
= 38760
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