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Math Help - how many tickets should I have

  1. #1
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    how many tickets should I have

    Hi,
    I am new to this forum and please excuse my grammer as I am not good enough at Mathematical terms.

    To win the first prize in lottary 6/49 we have to have 13.983.816 tickets ok ?
    if I played all those tickets and win the first prize. how many 5 winning tickets and how many 4 winning tickets I have ? What is the simple formula for that ?

    My second question is that how many tickets can I play(write-fill ??) if I have one (1) lucky number and how many tickets if I have 2 lucky numbers.
    (by "lucky number " I mean the number which I am sure to drop? )

    thanks
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  2. #2
    MHF Contributor matheagle's Avatar
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    I'm not sure what you're asking.
    It seems that you need to pick 6 out of 49 numbers (without replacement) correctly in order to win.

    {49\choose 6}={(49)(48)(47)(46)(45)(44)\over 6!}

    which is 13,983,816 so I guess I understand that part.

    I'm not sure what
    5 winning tickets and how many 4 winning tickets
    means
    I guess you want 5 correct numbers and that is 49 choose 5.
    Last edited by matheagle; June 2nd 2010 at 02:21 PM.
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  3. #3
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    For the benefit of those of you who didn't spend the afternoon sipping tea, this is a question on the UK national lottery.

    The lottery draws 6 balls at random (without replacement) from a pool of 49.

    Prizes are awarded for matching:
    3 balls
    4 balls
    5 balls
    6 balls

    He seems to ask:
    "If i buy 1 ticket for every possible combination, how many times will i win the 5 ball prize"
    which is  ^6C_5 * 44= 264
    Reason: Out of the 6 correct balls, there are  ^6C_5 sets of 5 balls you could match. For each of those you could pick any one of 44 values for the last ball

    "If i buy 1 ticket for every possible combination, how many times will i win the 4 ball prize"
    which is  ^6C_4 *45*44= 29700


    The question about lucky numbers:
    i think he means


    editincorrect formula fixed
    "if i am sure that 1 number will drop, how many different ticket combinations are there that i can buy? (ie how many possible outcomes of the lottery are there)":
    If you know the value of 1 ball, the lottery is just choosing 5 balls from 48:  ^{48}C_5 =1712304

    Try and do "2 lucky numbers" on your own
    Last edited by SpringFan25; June 2nd 2010 at 12:20 PM.
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  4. #4
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    Thanks matheagle for your reply,
    ok. if I pick 13,983,816 tickets ,I win the biggest prize..meanwhile I am paid because I have 5 correct numbers and 4 correct numbers.. how many winning 5s and 4s are there ?

    is this the formula ? 49/5(!) =635.628 which is to many or 13.983.816/635.628=22 5 winning tickets?
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  5. #5
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    that question was already answered
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  6. #6
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    Thanks for SpringFan25,

    His reply is what I am after ,

    you are great..
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  7. #7
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    Hi springFan25,
    in 49/6 ,say I have two "lucky numbers" which are ,say 5,10 . I keep writting these two numbers till I get the biggest prize ..I change the the other four numbers so how many tickets should I have ? I should have less tickets because I have "two lucky numbers"
    so what is the formula ?

    thanks
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  8. #8
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    i made a mistake on the formula for the second question, i should have said:

    "if i am sure that 1 number will drop, how many different ticket combinations are there that i can buy? (ie how many possible outcomes of the lottery are there)":
    If you know the value of 1 ball, the lottery is just choosing 5 balls from 48:  ^{48}C_5 =1712304




    For two lucky numbers, you are just choosing 4 numbers from 47
    ^{47}C_4=178365
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  9. #9
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    Quote Originally Posted by SpringFan25 View Post
    i made a mistake on the formula for the second question, i should have said:

    "if i am sure that 1 number will drop, how many different ticket combinations are there that i can buy? (ie how many possible outcomes of the lottery are there)":
    If you know the value of 1 ball, the lottery is just choosing 5 balls from 48:  ^{48}C_5 =1712304




    For two lucky numbers, you are just choosing 4 numbers from 47
    ^{47}C_4=178365
    Ok.. That will help...a lot..
    Thank you very much
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