Combinatorics? Lottery, Canadians help?

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SUMMARY

The discussion focuses on calculating the total number of combinations for Lotto 6/49, specifically using the combinatorial formula \(\binom{49}{6}\). The user correctly applies the formula, resulting in 13,983,816 combinations. There is confusion regarding the number of drawn numbers, with a mention of five numbers, which is incorrect as Lotto 6/49 requires six numbers from a set of 49. The user also questions the inclusion of zero in the set, which is irrelevant as the Lotto numbers range from 1 to 49.

PREREQUISITES
  • Understanding of combinatorial mathematics
  • Familiarity with the formula for combinations, specifically \(\binom{n}{r}\)
  • Basic knowledge of factorial notation and calculations
  • Awareness of lottery systems, specifically Lotto 6/49 rules
NEXT STEPS
  • Study the principles of combinatorial mathematics in depth
  • Learn more about factorial calculations and their applications
  • Research the rules and structure of various lottery systems
  • Explore advanced topics in probability theory related to lotteries
USEFUL FOR

Students studying combinatorics, mathematicians interested in probability, and anyone involved in lottery analysis or game theory.

flyingpig
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Homework Statement



My professor gave us this problem, I asked him about it but he just dumped it on me by saying "check it out yourself".

Problem

Determine the number of all combinations of winning numbers for Lotto 6/49

The Attempt at a Solution



I read on wikia there are actually 5 numbers? I am not sure if they repeat...if it even matters from a set of 49.

So my guess is

[tex]\binom{49}{6} = \frac{49!}{6!(49-6)!} = \frac{49 \cdot48 \cdot 47 \cdot 46 \cdot45 \cdot44}{6\cdot5 \cdot4\cdot3\cdot1} = 13983816[/tex]

What's the problem? I don't know if 0 is in the set...
 
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flyingpig said:

Homework Statement



My professor gave us this problem, I asked him about it but he just dumped it on me by saying "check it out yourself".

Problem

Determine the number of all combinations of winning numbers for Lotto 6/49

The Attempt at a Solution



I read on wikia there are actually 5 numbers? I am not sure if they repeat...if it even matters from a set of 49.

So my guess is

[tex]\binom{49}{6} = \frac{49!}{6!(49-6)!} = \frac{49 \cdot48 \cdot 47 \cdot 46 \cdot45 \cdot44}{6\cdot5 \cdot4\cdot3\cdot1} = 13983816[/tex]

What's the problem? I don't know if 0 is in the set...

Check out the page http://www.olg.ca/lotteries/draws_faq.jsp and look at the faq.

RGV
 

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