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Math Help - Basic 11+ question but need help

  1. #1
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    Basic 11+ question but need help

    Please Help,

    Would appreciate easy workings as I have to explain answer to my 10 year old daughter.

    Q
    The last part of a telephone number has four digits,e.g

    7814 1487 2103 2772

    The last part of the tel number can start with any digit apart from zero. The other three digits can be any number. How many four digits are there?
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  2. #2
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    Four digit numbers

    Hello
    Quote Originally Posted by dee@landspace.co.uk View Post
    Please Help,

    Would appreciate easy workings as I have to explain answer to my 10 year old daughter.

    Q
    The last part of a telephone number has four digits,e.g

    7814 1487 2103 2772

    The last part of the tel number can start with any digit apart from zero. The other three digits can be any number. How many four digits are there?
    The easiest way to explain it might be something like this:

    If we start counting at zero, and stop when we get to 9, how many numbers have we counted?

    That's 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

    The answer isn't 9, is it? It's ten. That's because we started at zero, not at one.

    If we counted from 0 to 99, how many numbers would we have counted? It's not 99 - it's 100. (Because we're counting from zero again.)

    In the same way, if we count from 0 to 9,999, how many numbers do we count? The answer is 10,000 - not 9,999 - because we've got to remember to count the zero.

    If we wanted to write down all the telephone numbers that we could think of that have 4 digits, we could start writing at 0000, then 0001, then 0002, and so on all the way up to 9999. But that would be just like counting from 0 to 9,999. And we have just said that there are 10 thousand of these numbers.

    But, hold on, we were told we couldn't begin with a zero, so we shall have to leave out all the numbers we just pretended to write down if they begin with zero. These will be all the numbers from 0000 to 0999. How many of those will there be? Well, this is just like counting numbers from 0 to 999 - and there will be one thousand of these.

    So, out of our 10 thousand telephone numbers, we are not allowed to count one thousand of them, because they begin with zero. That leaves 9,000 that we are allowed to count.

    How does that sound?

    Grandad
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  3. #3
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    Grandad,

    Thank you very much. Is there a formula I can use as in permutations and combinations?

    Thanks one again

    Deee
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  4. #4
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    Perms and coms

    Hello Dee
    Quote Originally Posted by dee@landspace.co.uk View Post
    Grandad,

    Thank you very much. Is there a formula I can use as in permutations and combinations?

    Thanks one again

    Deee
    Yes, but I was trying to avoid it! If I were doing this question on an A-level paper, I would answer it like this:

    There are four spaces that are to be filled. The first must be a digit from 1 to 9. This can be chosen in 9 ways.

    The second space can be filled by any digit from 0 to 9. So this space can be filled in 10 ways.

    Similarly the third and fourth spaces can each be filled in 10 ways.

    So, using the r-s Principle (the fundamental principle of combinatorics), the total number of ways of filling all four spaces, one after the other is

    9 x 10 x 10 x 10 = 9000

    I don't think I'd use that method to explain it to a 10-year old. But you could try!

    Grandad
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  5. #5
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    Dear Grandad,

    All I can say is you should be called The Guru.

    Thanks

    Dee
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  6. #6
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    Thanks

    Thanks, Dee, for your kind comments.

    Grandad
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